The experiments have been done by Roderich W. Graeff , and he claims to have successfully confirmed the Loschmidt Effect. The document outlining his experimental work and some background is here. The proceedings of the AIP are available (to buy) here. Graeff’s website is here.

The results and methodology are Critiqued by D.P. Sheehan who thinks the energy flow should go the other way but doesn’t seem to have done any experiments to try to prove it. The critique is here (page 1) and here (page 2) and here (page 3).

So what does this mean for the Nikolov – Zeller Unified Theory of Climate? And what does it mean for the claims of warmists that it is the radiative flux which supports the adiabatic lapse rate? Why has this enduring mystery not been attended to more carefully by mainstream science? After all, knowing whether the lapse rate in the atmosphere is due to radiative effects or gravitational effects seems at first flush to something quite fundamental to our understanding of the physical world we live in. Enquiring minds would like to know the answer!

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“Presumably, one could drive a heat engine with this gradient, thus violating the second law.”

-But presumably the heat engine itself (solid, liquid, or gas) would, necessarily, also span the precise same gravity gradient [hot source to cold sink], and so the net effect would be zero, and no extractable work?

There seem to be two gradients involved in the Earth’s atmosphere as opposed to the experimental device proposed.

i) A gravitational gradient with gravity increasing from top to bottom.

ii) A thermal gradient with temperature decreasing from bottom to top.

I’m pretty sure that in reality the upward flow of energy from surface to space (hot to cold) would vastly outweigh any tendency for gravity to pull energy downward via some sort of convective process.

Is this proposition that energy is actually pulled down by gravity via conduction from higher up in order to increase the temperature at the base ?

I always thought that the reason for a higher temperature at the base was higher density, more collisions and thus a longer delay in energy escaping upwards due to the obstruction provided by the colliding molecules.

The lapse rate has everything to do with gravity and nothing to do with radiation. The clue is that g appears in the formula! You get a lapse rate g/Cp in a gas heated from below by a hot lower boundary.

Not sure about the Loschmidt effect – it is incorrect according to the standard equations of heat transfer. Maybe it doesn’t matter because being a conduction effect it would be extremely slow on atmospheric timescales, so swamped by other heating mechanisms.

Not sure this proves much either way. The experiment was done in an enclosed cylinder, while our atmosphere is only fully bounded on at the bottom, semi-bounded by the ionosphere/magnetosphere at the top and is almost unbounded for 360 degrees to the side – depending on geography and small directional constraints from the Coriolis effect.

In my view, the reason for the reduction in atmospheric temperature with altitude is that the air near the surface of the earth is at a higher pressure and is denser. Therefore there is more chance of outbound or inbound photons hitting a molecule than there is higher up, which in turn equates to a more efficient transfer of kinetic energy.

There is a temperature decline with a pressure decline to a certain point, and then a temperature increase with a (practically) minimal pressure decrease (as the air pressure is already very low).

The energy content of the atmosphere is a function of mass and temperature. The energy content of a given volume of atmosphere is a function of density and temperature. I can’t plot how these two parameters change: does the energy content of the atmosphere decline more regularly and ex-plain any of the energy rather than heat flow?

” And what does it mean for the claims of warmists that it is the radiative flux which supports the adiabatic lapse rate?”
My meteorology training was a long time ago, but afaik the adiabatic lapse rate ( dry or wet) is the rate with which a parcel of air changes its temperature with increasing (or decreasing) altitude, WITHOUT exchanging heat with the surrounding air.
The temperature gradient of the atmosphere is just that, the change of the temp. with increasing altitude. Can be even positive when a so called inversion exists.
The temperature gradient (or lapse rate) has nothing to do with adiabatic imo.

Isn’t in a stable atmosphere the total energy of each particle the same, irrespective of altitude?
I mean the sum of thermal and potential energy.

Tenuc: Unbounded to the side? What side? There’s an underside (the surface) and a topside (the magnetosphere) as you said. Try as I might, I can’t find another unbounded ‘side’ though.

Doug: “The energy content of the atmosphere is a function of mass and temperature.”
I think in terms of ‘stuff’ like vibrating and colliding molecules. Temperature seems to me to be a symptom of the real quantities, rather than a fundamental that other things ‘are a function of’.

Stephen: Your two points can be reformulated as:
i) A gravitational gradient with gravity increasing from top to bottom.
ii) A thermal gradient with temperature increasing from top to bottom.

In terms of stuff, upward trajectories are retarded by gravity, so providing less excitation to molecules above through collision. The converse is true too. So more energy ends up at the bottom.

Paul: As Hans tells us on the Jelbring thread, energy and temperature are not the same thing.

Sorry folks, this sounds like a pulse jet modified steam engine that goes up at first. Acceleration, creating an artifical compression thru a one way exhaust, dang, an early german rocket, or the early kerosene oxygen rockets where the exhaust came out of the front end, I can picture it, just cannot remember who did it, Goddard/Van Braun? 1930’s.

tallbloke says:
January 4, 2012 at 10:18 pm“…Tenuc: Unbounded to the side? What side? There’s an underside (the surface) and a topside (the magnetosphere) as you said. Try as I might, I can’t find another unbounded ‘side’ though…”

Sorry, Rog, not very clear, I should have phrased that better.

A parcel of air in an enclosed cylinder it is fully bounded, top, bottom and sides. In the atmosphere the same parcel of air is bounded top and bottom, but can freely move to the side in any direction, unless a large building or a mountain constrains its movement. Thus the hard cylinder experiment has limitation versus what happens in the real world.

“There seem to be two gradients involved in the Earth’s atmosphere as opposed to the experimental device proposed.
i) A gravitational gradient with gravity increasing from top to bottom.
ii) A thermal gradient with temperature decreasing from bottom to top.”

Actually there is only one gradient that we need to concern ourselves with, the thermal gradient. The gravitational gradient is so small that it can be ignored within the troposphere. At 10 km the gravitational acceleration (g) is 99.7% of the g at the surface. There is almost double that variation in g in going from the poles to the equator due to the equatorial bulge.

Stephan also says,

“I’m pretty sure that in reality the upward flow of energy from surface to space (hot to cold) would vastly outweigh any tendency for gravity to pull energy downward via some sort of convective process.

Is this proposition that energy is actually pulled down by gravity via conduction from higher up in order to increase the temperature at the base ?

I always thought that the reason for a higher temperature at the base was higher density, more collisions and thus a longer delay in energy escaping upwards due to the obstruction provided by the colliding molecules”

Most of the posts thus far are dealing with similar issues. Maybe I can help.

First, gravity does not pull down energy. Gravity is simply a downward vector force on mass. When that force causes a deflection in the mass (e.g., compression), energy is generated (in this case work energy). Second, density is not the cause of anything, it is simply a result. The emphasis on density is an artifact of working in units of moles instead of units of mass. I will explain.

The first law for a gaseous atmosphere can be written:

dU = dQ – dW = dQ – PdV (1)

The differential for the work term is PdV since the atmosphere is a constant pressure system and VdP = 0. The sign for PdV is negative since I am assuming that work is being performed by the system to the surroundings. Let’s also specify that all terms are expressed as intensive properties (Q is in joules per unit mass and PV is an intensive property in its self – no moles allowed here).

We can also say that dQ = CvdT so that equation (1) becomes:

dU = CvdT – PdV (2)

But this assumes that the system is only influenced by one field, the electromagnetic field (the sun). But the atmosphere is also influenced by a second field, the Earth’s gravitational field. Thus we need to add another term to the first law to reflect the gravitational field:

dU = CvdT + gdz – Pdv (3)

If we assume that the atmosphere is at static or dynamic equilibrium (and all politically correct climate scientists must – rightly or wrongly), then dU = 0 and:

CvdT + gdz – PdV = 0 (4)

If we define the system described in (4) as an air parcel, then certain things must happen if any of the terms become > or 0) and the parcel will expand (dV > 0) doing work on the surroundings. But that work energy (PdV) must come from the existing internal thermal energy (CvdT) thus leaving CvdT smaller (cooler) than it would have been if expansion did not occur. At the same time the parcel, having expanded, becomes buoyant and rises. That work energy is now converted to gravitational potential energy (gdz). The internal energy (U) of the parcel is still the same as it was when it first received heat energy from the surface but CvT is now smaller and gz is larger (an isentropic or adiabatic process). The density is also smaller because the parcel expanded (but who cares?). This process continues as long as the parcel rises.

The opposite scenario can occur if an elevated parcel is cooled (from radiation to space?): the thermal energy is decreased (CpdT), the parcel is compressed (+PdV) from the mass above it and it descends, and the gravitational potential energy (gdz) decreases. But the total internal energy (U) remains constant as it descends (isentropic/adiabatic process). The density is also larger due to volumetric contraction (but who cares?).

Since CpT = CvT + PV for an adiabatic system, equation (4) can also be rewritten as:

CpdT + gdz = 0 (5)

And some quick algebra yields:

dT/dz = -g/Cp (6)

which is the classic formula for the dry adiabatic lapse rate. (This also explains why Cp and not Cv is the correct term for the Loschmidt equation).

So the thermal gradient observed in the atmosphere is nothing more than the result of the conservation of energy via isentropic processes (constant entropy) with PV work driving the processes. The Helmholtz free energy is zero and the system is at equilibrium (U = constant) even though a temperature gradient exists.

Temperature is only a measure of one form of energy in the atmosphere and thus can only be a partial descriptor of the atmospheric thermodynamics. For example, at 10 km height, gravitational potential energy accounts for 30% of the total internal energy (based on the 1976 Standard Atmosphere). And if we are dealing with a moist atmosphere, we have to include a term for the latent heat of vaporization, which can be a very sizable number in itself.

Since radiation heat transfer only deals with one term of the first law (CvT), it cannot adequately be a primary predictor of atmospheric behavior. The radiative properties of the atmosphere are a function of the non-radiative processes occurring in the atmosphere, not the other way around.

There are some subtle points here that need addressing. William Gilbert’s post touched on one, and BenAW touched on it as well.

For a dry atmosphere, the thermal energy and gravitational potential energy in any given air column wind up being the same, a 1:1 ratio regardless of what the surface temperature is. However for a moist atmosphere there is a subtle disproportion. Thermal energy (which includes latent heat) accumulates faster than gravitational energy for a given rise in surface temperature.

This creates some very vexing problems in terms of accounting for energy. The 1:1 relationship is actually the virial theorem, which is also used to understand the atmospheres of stars. If the atmosphere of a star heats up, it expands by a predictable amount. To have a nonlinear relationship (in a moist atmosphere) means that a lot of simple analytical techniques cannot be used. We need to know the function form of the relationship, and we don’t.

I realized two years ago, reading arguments on RealClimate and elsewhere about Miskolczi’s use of the virial theorem, that this particular problem had never been solved. Instead it seems that the method was to bypass the question by assuming the atmosphere is hydrostatic. If it’s hydrostatic, the potential energy never changes. Since the ratio is fixed for a given amount of potential energy, the thermal energy doesn’t change either. So the two can be lumped together as “available energy”.

It’s a shortcut, a cheat, that only works so long as the atmosphere really doesn’t expand or contract over the long term. But of course if you’re going to postulate CO2 warming the Earth over its entire surface by an average of 3 K or 1 percent, the atmosphere is going to EXPAND by something like 1 percent, and PE will change, and so will KE.

And thus we get massive confusion when the IPCC models effectively mandate that the atmosphere is hydrostatic. It will WARM, but it won’t EXPAND. (This is a slight oversimplification. I give a much fuller explanation in my ‘Pot Lid’ paper on my blog.)

If you want to make sense of the vertical air column, you have to first solve the question of whether adding water vapor increases or decreases gravitational potential energy, and by how much. That is an historic failing of climatology. I would be very interested in comments on whether my essay succeeds in answering it.

William and Dean, thank you both very much for these contributions. You have both advanced and clarified my understanding of basic atmospheric processes (though I still have some way to go). I think we should continue the discussion here to keep it all together for now, but I’d like to do follow up posts on both of your research efforts in due course.

I think this might be the right place to re-introduce a correlation graph I did a couple of years ago which I’m still looking for an explanation for. This shows the global specific humidity near the tropopause at 300Mb (NCEP re-analysis of weather balloon data averaged over 96 months in red) against sunspot number (SIDC – roughly equivalent to TSI – total solar irradiance in green).

Why might changes in solar activity (averaged here over 96 months) have such an effect on specific humidity? People keep telling me that the balloon data is of questionable quality, but the clear relationship here tells me it might not be so bad after all. I tried to get Ferenc Miskolcsi to give me some feedback on this, but I couldn’t get him to offer any opinion. Maybe because it is a feedback to an external forcing which doesn’t fit his schema?

What effect might the change in specific humidity up at the 300mb level have? My total guess is it would probably affect levels of high cloud. Might this be part of the mysterious amplification of solar activity variation identified by Nir Shaviv in his paper on using the oceans as a calorimeter?http://sciencebits.com/calorimeter/

“But what are the temperatures? That causes me to ask, what about the speed of the molecules within such a static column of the atmosphere. (notice, I made it static to remove local effect here for simplicity as convection, evaporation, absorption) To me the molecules must all have the same speed all of the way up the column or they would be out of equilibrium and would eventually correct this imbalance. And everyone should be saying to themselves… it only depends on the total energy within a column, but, we really all knew that!”

Does that statement have some tie to this one being posted? They sure are speaking of the same principles. In fact, I think that is dead center on that whole concept and I would have to agree with Maxwell and to me Boltzmann should have known it’s impossible.

Just look very close at the molecular speed. That simple. And relate that to exactly what temperature ‘is’. What pressure ‘is’. What density ‘is’. How could a column (static and in thermal equilibrium that is) ever have molecules that were not at the same mean velocity? Makes no sense right? That is why the velocity is the very bottom on the dependency chain.

One thing pressure depends on is this mean velocity. Of course it also depends on the closeness of the particles and their mean mass each but the mass term is affected by gravity and that puts gravity also on the bottom of the dependency chain. Nothing affects gravity but the mass of the entire earth system.

And density is dependent solely on the spacing of the molecules in a specified volume. Pressure and density share that same aspect property, the particle spacing, how close they are to each other on the average.

Now temperature with height. ….. If your like me most might pause here. You now have a whole bunch of base units and ALL OF THEM affect the temperature hold all others constant. T = PR/ρM. Many jump here to lapse rate but lapse rate is a funny parameter. It in one respect is not real, it’s a descriptive parameter, just a ratio, but the ratio is real and meaningful. This is where my mind gets a bit foggy and I’m glad such great minds as Maxwell and Boltzmann didn’t just jump out with the true answer either, but I do think it traces itself all of the way back in any serious analysis to the mean velocity of the particles. That is where I always end up, constant velocity, therefore, constant energy per mass and mass increases as you go down from the top of atmosphere toward the surface. Therefore you could no have a heat engine without differences in MEAN VELOCITY, not energy.

See my point? I have thought of this a few years ago but totally unrelated to climate.

Bet someone is going to raise I didn’t include area in pressure, height in gravity, your right. The area was implied by being a column and gravity would have a tiny change, I did ignore it. Just look at the overall thoughts, fill in or ignore the irrelevant points please.

This is one of the areas of physics I find so fascinating. Lots of interaction in the terms.

Wayne, I think I get your point about the impossibility of a perpetuum mobile of the second kind, despite the gradient. Particles near the top of the column have more energy because they have more gravitational potential energy, but in equilibrium, this energy is not manifested.

Surely Loschmidt’s point though, is that in a real-time dynamic system, with solar energy flowing through the system, there is a downward flow of energy due to transfer of gravitational potential between molecules which favours transfer of larger energies from particles being accelerated downwards hitting their neighbours below, as opposed to smaller collisional energies being transferred upwards due to retardation of the molecule’s velocity by gravity.

This gravito-thermal effect is counteracted by upward convection (maybe extra radiation too?) in the real atmosphere but still causes a gradient because of the work done to overcome it.

I’m not sure I expressed that too well (woolly brain since the big crash) but maybe it’ll stimulate more thoughts from clearer minds.

Tallbloke, you just brought in many terms, convection, radiation, and I’m still back the beginning, that must be what little physics is in me. First answer my question, is there any way within a vertical column under gravitational pull, with a solid bottom, static, totally insulated, no energy going in or out, in equilibrium, it’s been standing there 10km high for a million years (hypothetical), are all molecules at the same mean velocity. Could they ever be different in that case? That is such a key question to me, and, should be to you also if you’ve never thought at that particular level. What do you think? Anyone can chime in.

Then I’ll go deeper if we can get parallel on that question. Everything else depends on it, also on NZ’s theory.

Wayne, you’re right, I’m running before I learn to walk, it was stupid of me to start dragging other puzzles into this thread, where we need clarity on basics.

Regarding your question; Since there has been no empirical observation which can describe the situation, it seems to me that it comes down to belief. Do you believe in the tendency to maximum entropy in a world where the gravitational field is always active?

This was Graff’s point. The second law holds when there are no fields crossing the boundary of the system you define as isotropic. But on Earth, that is never the case, because gravity pervades, and it is directional, not isotropic.

Graff’s experimental results are what they are, whatever we might speculate is going on at a level we are unable to observe. So he modified the second law to accomodate the results. Given that we don’t know what causes gravity, I think he may have a point.

His reformulation of the second law of thermodynamics is:

In isolated systems – with no exchange of matter and energy across their boundaries AND WITH NO EXPOSURE TO FORCE FIELDS – initial differences of
temperature, densities, and concentrations in assemblies of molecules will disappear over time, resulting in an increase of entropy.

Sorry, moving too fast and I didn’t read your link to Hans before writing that last post. I do see one thing I should have made clear, the energy I was speaking of near the last paragraph was really energy density, not the absolute quantity of column energy. Seems Hans and I are saying basically the same thing, it’s just I went microscopic as . he . advised . not . to . do, oops. But my analysis above does seem to end at the same point, all mean velocities *are* the same and as Hans showed, temperature must rise with density and pressure. Thanks, got that answered. Now need to check and settle a few things on paper.

I am current working on mapping the velocity of the planetary tilting.

If we just had straight rotation of the planet, the circulation of heat and cold would be stationary at different latitudes and not move around.
We would not have any water either as the equatorial region would have been too hot and boiled.

Planetary tilting effects the planet and oceans very little.
It does have a huge effect on the heat movement in the atmosphere. Moving the planet into areas back back tilting where sub zero was by lack of solar radiation.

Thank you for a clear summary of the physics, and for the reference to your paper, which I hope has received widespread attention.

The outstanding conclusion (to me) is: “The radiative properties of the atmosphere are a function of the non-radiative processes occurring in the atmosphere, not the other way around”. If climatologists could only accept this, rather than going to extraordinary lengths to model “back radiation” in GHMs (that can neither be validated nor verified) we could at last have some common sense in this debate – in my personal opinion.

“Isn’t in a stable atmosphere the total energy of each particle the same, irrespective of altitude?
I mean the sum of thermal and potential energy.”

Exactly and you said it in a very concise way. (You might exchange “particle” with a small amount of atmospheric mass, about a billion molecules). This is what meteorologists always have been tought since about 100 years. The dry adiabatic temperature lapse rate (-9.8 K/km) is observed in our real atmosphere (before the age of AGW) during favourable physical conditions such as:
A. During afteroon after strong solar irradiation over land areas. Many birds know about this.
B. Katabatic winds falling downslope from the Antarctic high altitude areas. The highest average windspeed is found around the coast of Antarctica.
C. In special cases “behind” mountain ranges where Chinookes can be observed and the temperature can increase 20C in 20 minutes during winter time. They can be found in the denver area.
D. The static case can be experience best at Colorado river in Grand Canyon where the temperature can be +50C during summer time. The plateau at +2000 m elevation might become 35C and add STATIC adiabatic heating of +15 since the river is about 1500m below the plateau.
Nonmeteorologists have hard to grasp the theory behind the facts above and most meteorologist in the bandwagon deny these observational facts that easily can be checked.

The reason why our real average temperage laspe rate is around -6.5k/km instead of -g/Cp -9.8 K/km is simply that the atmosphere is constantly disturbed by physical processes that prevent equal energy to exist all the way up vertically up to the tropopause.

@tallbloke says: Your graph above of humidity vs. SSN it is an image worth a thousand words. It is such a simplicity many reject. It is simply the obvious WATER CYCLE. It´s the Sun…!
We have to revisit the primary school “water cycle” , stripping from us the enormous baggage charge of “knowledge” and self indulgence, as you have done.
We all know “humidity”, water vapor, defies gravity and goes up, as we see everyday when preparing our daily coffee, until it falls down again as fresh rain.

Hans, I appreciate your reasons for dealing with ‘macro sized air parcels’ rather than individual molecules, but please could you help clarify something for me regarding the summary of Loschmidt’s hyothesis given by Sheehan at the top of this post, in order to help us reconcile your macro view with Wayne’s molecular view.

Sheehan says that Loschmidt is postulating a net flow of energy transferred downwards by conduction. You seem to be saying the air packets at high altitude near the tropopause have around 33% of their energy locked up in gravitational potential and so less of their energy is thermalised to be measurable as temperature. But is this not equivalent to saying that gpe-amount is a ‘property’ of the air packet, which doesn’t require any physical mechanism to transfer anything anywhere? How does the ownership of gpe ’cause’ there to be less thermalisation? Less collisions because of lower density?

Hans says “The reason why our real average temperage laspe rate is around -6.5k/km instead of -g/Cp -9.8 K/km is simply that the atmosphere is constantly disturbed by physical processes that prevent equal energy to exist all the way up vertically up to the tropopause.”
But, is not the reduced lapse rate due to the condensation of water vapor releasing heat. The 9.8 K/km is called the dry adiabatic lapse rate. The alarmists ignore (or minimise) the transfer of heat at the surface by convection and phase change. The only heat loss by radiation from the surface (on an average yearly basis) is the 66W/m2 window which has been determined (rightly of wrongly) by satellite measurement.

Cooling happens through rain, storms, hurricanes, which by discharging the electric charge of water vapor change its molecule arrangement from H-OH (hydrogen hydroxide) to H2O (di-hydrogen oxide: Water, rain drops). The same phenomenon is observed in any chemical precipitation of oxides out from hydroxides. (Note: Hydrogen is a solid metal at almost 0ºK), and anyone can check it.

Any examination of the behavior of a column of air should consider the energy at the molecular level. O2 & N2 are almost transparent to incoming solar radiation and somewhat opaque to infrared, think glass coming in and insulation going out. The more dense the air the slower the infrared radiation back out to space. Incoming solar radiation energizes some of the air molecules it passes through there and are more of them to contact as the air becomes denser. In coming radiation is more effective energizing the more dense air at the surface and the more dense air is more effective at slowing the re-radiation back to space. Energized molecules expand in the space they occupy and therefor “weigh” less in that space then their less energetic neighbors so they therefor rise into a less dense level. The temperature of any fluid is the average of all the molecules. Some are much more energetic the others in any non ideal , real, volume. They will try to stratify with the cooler at the bottom and the hotter, more energetic, to the top. Water molecules are much more active in their of change conditions due to energy changes then O2 & N2 of the atmosphere. They become gas and take up more space at temperature, then other atmospheric gasses, rise to the point of condensation and then take up much less space. The water active section of the atmosphere is much different in behavior then the part that is water poor. pg

Thank you Tallbloke (and I hope that you have got your computers back now!)

I have long held the opinion that the “climate” of the Earth can be adequately explained by insolation, gravity, rotation, the mass of the atmosphere and the phase changes of water. The laws of physics as a whole, rather than just radiative physics, must be applied properly. I like the concept that radiative atmospheric physics is a consequence – not a cause – of the overall conservation of energy in a system in (temporary) equilibrium. The problem is how to articulate this concept, in order that policy makers can understand it.

In my personal opinion (further than the basic physics considerations discussed above) the CAGW hypothesis rests upon two broken hockey sticks – the Mannian temperature one (thankfully debunked) and the carbon dioxide one (reliant upon the probably flawed methodology of ice core analysis, rather than the historical evidence of chemical analysis). When all of these factors are taken together the CAGW hypothesis vanishes like the morning mist.

It probably goes without saying that I believe that anything that humanity does (eg. doubling, or tripling the 0.04% of CO2 in the atmosphere) will have no measurable effect on the climate at all.

@P.G: A chemical analogy of “gravity”: “For example, in the self-ionization of water we see that two water molecules collide to react and form a hydroxide ion and a hydronium ion. Each reaction begins first by an electrostatic attraction between an electron rich and an electron poor region of the reactants…http://www.chem.ucla.edu/harding/notes/notes_14C_str&react.pdf
Then, the more charged a gas, as you say properly, molecules expand in the space they occupy and therefore “weigh” less in that space then their less energetic neighbors so they therefor rise into a less dense level
Vibrations accommodate themselves according to its “pitch”, to its frequency. I do celebrate the harmony of Tallblokes´ Agora of thinking; it means a higher energetic level, where it “weights” less in that space then their less energetic neighbors:-)

“I’m pretty sure that in reality the upward flow of energy from surface to space (hot to cold) would vastly outweigh any tendency for gravity to pull energy downward via some sort of convective process.”

You might claim that my comment below is out of context and you might be right. However I would like to exemplify that big real energy flows exist from upper part of the troposphere to the surface of earth. This happens just now in the area above the polar circle (average outgoing radiation to space is around 150 W/m^2).
There is no solar energy heating the atmosphere so ALL energy provided to the atmosphere has to be carried by winds from southern areas to the surface of earth or rather the lowest level of the atmosphere. A common temperature might be -20 to -30C. If there is a 1 m snow cover almost no energy is coming from beneath.

The physical processes at hand are A. advection (horisontal convection) fronm south, B. downward vertical convection in polar areas (subsidence) which is prominent and C.local downward net IR radiation. The interesting fact is that much of this atmospheric motion is driven by the rotation of earth and extreme local IR-radiation to space (no clouds) which produce Mobile Polar Highs or MPH. These are very big dense heaps of cold air that can be built up for a week and then starts mowing towards the equator and might not come to rest before reaching the equator. These phenomena have been examined by the late professor Marcel Leroux and dr Alexis Pommier, both French. Their important results have consistently been ignored by IPCC.

Just wanted to mention that the downward energy flow is real and sometimes the dominating process(es) to warm surface air (even if it is cold air)

@Hans; I do take exception to the statement that “There is no solar energy heating the atmosphere” I can assure you that there is solar heating of the air even when the sun is over the horizon.
There is a measurable heating of the air even with a meter of powder snow on the ground before the sun rises above the horizon.

@Adolfo perhaps we need to explain harmonics of frequency and atomic size in the transfer of energy both per atoms and molecules. 8-) pg

You are probably delivering a verification of a hypothesis I have about terrestrial – extraterrestrial connections.
It is obvious that the sunspot cycle is filtered but the humidity curve seems unfiltered? I would like to know if you can calculate correlations.
In that case I would like to know the correlations of both unfiltered values and filtered values. I assume that you would use yearly values for both correlations?
It might be best If you sent me the raw data.

“However I would like to exemplify that big real energy flows exist from upper part of the troposphere to the surface of earth”

I do accept that. My comment was as regards a situation undisturbed by other processes as in the isolated container.

I recently commented at WUWT along the lines that I think the role of radiative processes is as a mopping up exercise if the non radiative processes fail to do a complete job of equalising energy in with energy out.

That implies radiative phenomena as a consequence of non radiative processes (not vice versa) which is similar to what William Gilbert said in this thread.

“The radiative properties of the atmosphere are a function of the non-radiative processes occurring in the atmosphere, not the other way around”.

@Hans I don’t know where you stand but where I sit it is a noonday sun on a clear day at 40 degrees north in early January. As to the percentage of solar flux that hits the ground today I don’t know. It is a nice 72F day at 2200ft elevation.
Sorry about being smart arsed, 8-) it happens sometime.

1. “Why might changes in solar activity (averaged here over 96 months) have such an effect on specific humidity?”

2. “What effect might the change in specific humidity up at the 300mb level have?”

As for question #1, I may have an answer to half the question. The title of my 2010 E&E paper is “The Thermodynamic Relationship between Surface Temperature and Water Vapor Concentration in the Troposphere” (see the link above). If the assumption can be made that surface temperature is at least partially affected by solar activity via variation in cloud cover (Svalgaard’s hypothesis) or some other process, then my paper explains, hypothetically and empirically, why higher surface temperature results in lower specific humidity in the upper troposphere.

A short summary is that a higher surface temperature results in a higher near surface specific humidity (Clausius-Clapeyron relationship). If or when convection occurs, the higher humidity parcel will release a greater quantity of latent heat upon condensation. The thermal energy generated from latent heat release is translated into both thermal energy (CvdT) and work energy (PdV) (see my post above). But I found that the larger the quantity of latent heat released, the greater the percentage of that latent will be converted to work energy (PdV) as opposed to thermal energy (CvdT). (This is where assumptions of system equilibrium by climate scientists lead to a lousy understanding of the system dynamics). My empirical data showed that between 40% and 80% of the latent heat will be converted to PV work, with the highest surface temperature/specific humidity system yielding the higher PV work percentage. As a result, the greater the rate of PV expansion, the greater is the convection rate. A faster rate of convection results in a greater efficiency of condensation of the remaining water vapor. The higher the PV/thermal energy ratio, the more complete is the condensation in the parcel, and the lower the specific humidity will be at higher elevations.

PV work energy is very important in atmospheric thermodynamics, but most climate scientists seem oblivious to its existence. They seem to get the “thermo” but miss the “dynamics”. Where is the arrow for PV work energy in the Trenberth energy balance chart? Where is mass transfer? (By the way, gravity also plays a major role in this process).

As for your question #2, the standard answer is that the lower the upper troposphere water vapor concentration, the lower the effective emission height which results in a lower surface temperature (and vice versa). But that is looking at the system from a strictly radiative standpoint – the “thermo” part. But if you also consider the “dynamics” part, the role of increased PV work to generate the lower humidity also results in an increase in the maximum convective height. (This also suggests a higher tropopause). And the higher convective height means a warmer temperature at altitude from the greater release of latent heat. This should also increase outgoing LWIR. All of this, of course, has its greatest impact in the tropics which will affect the advective transfer of heat to the higher latitudes. And I’m sure cloud formation plays a role but I’m not sure anyone completely understands it.

You are correct. The differential equations I am using are thermodynamic process equations and not thermodynamic equations of state. There are several process paths that can be taken to get to a given equation of state. I probably should have used the term “intensive variable” or “intensive quantity”.

Hans, thanks for your interest. I’m more than happy to pass the data over to a professional for assessment. The laptop that the data is on is in quarantine at the moment, but I’ll find the links to the data sources and send them to you.

William, that’s very interesting. I wonder if there might be some confounding with ENSO. There have been big el nino events near solar minimum for the last 50 years. I would expect that would push a lot of extra water vapour into the lower tropical troposphere. As you point out, higher humidity lower down results in lower specific humidity higher up. That all fits together. I wrote an article on the timing of ENSO and the solar cycle a while ago. Nothing fully conclusive, but some good ideas were pushed around.

wayne says:
January 5, 2012 at 9:13 am“…First answer my question, is there any way within a vertical column under gravitational pull, with a solid bottom, static, totally insulated, no energy going in or out, in equilibrium, it’s been standing there 10km high for a million years (hypothetical), are all molecules at the same mean velocity. Could they ever be different in that case? That is such a key question to me, and, should be to you also if you’ve never thought at that particular level. What do you think? Anyone can chime in…”

Hi Wayne, interesting thought, but what does this mean regarding the real world atmosphere?

The real world is a messy place with lots of photons whizzing about and bashing into things, not to mention variable amounts of water vapour transferring energy around in various ways. This is my big gripe with Graeff’s experiments, it is comparing chalk and cheese, and the results have little meaning regarding actual weather/climate systems. Huge open systems are not comparable with small closed lab experiments.

Your re-post of the specific humidity vs. SSN graph finally galvanized me into looking into this issue, and I’ve spent most of the day reviewing data from the NCEP/ESRL data set to see if anything popped out. What popped out, unfortunately, was that the ESRL data are indeed unreliable. I couldn’t check the specific humidity data, but as shown in [these]
there are major mismatches between ESRL and GISS for surface air temperature and between ESRL and UAH for troposphere and stratosphere temperatures, and there’s no reason that I know of to suppose that the specific humidity data will be any better. Sorry about that.

But at least it’s comforting to know that there’s someone other than me on this blog who looks at the data. :-)

I want to make an observation about William Gilbert’s paper. First, let me see if I can summarize his fairly lengthy argument in one sentence: As sea level air gets wetter, it will shed its latent heat closer to sea level, and will convert more of it to work rather than to increasing temperature.

This explains why relative humidity at sea level rises but RH in the upper troposphere actually falls. There is a negative feedback effect. As evaporation increases, the latent heat released increasingly goes to convection (causing packets of air to rise and expand) rather than to warming the air.

Assuming I haven’t butchered William’s argument with this summary, let me say I like this argument a lot, because if we pursue it just a little further, it seems to agree with my ‘Pot Lid’ argument fairly well.

My argument starts with the observation that the IPCC models neglect essentially all density shifts between modeled layers. This comes as a surprise to many people, but it is true. Evaporation for example is virtual, a model-within-a-model, following the guidance of a 1973 paper by Arakawa and Schubert. A GCM calculates the amount of H2O mass that is present, calculates the rising air mass, and transfers H2O from lower levels to higher ones, but it does not transfer any air mass. So thunderstorms with violent updrafts do not permanently or even temporarily move air away from sea level, they just move moisture and heat.

The problem with this is that a long-term warming trend necessarily involves transferring air from down near sea level, up to the upper third of the troposphere. if you draw the “before” and “after” density profiles for a given air column, density values will end up lower at sea level but higher near the tropopause. GCM’s cannot model transfer of density to the upper layers; the calculation just omits any such step. Over a long period (decades of modeled time) this leads to paradoxes like the “hot spot” in the upper troposphere, which is a universal feature of GCM’s but not observed in reality.

Now what I find intriguing is that William has shown that for especially warm conditions near sea level, there is a great deal of PdV work being done in the lower atmosphere, which reduces the temperature rise due to latent heat transfer.

I want to know William’s opinion on this point: What ultimate effect does that additional PdV work have? Where does the expanding air eventually wind up?

It seems to me that it must go up, and that it is converted to gravitational potential energy. There is a net shift in density from around sea level to higher up, that occurs whenever exceptionally high humidity and heat occur.

To put it simply, on typical days with moderate humidity and heat, the air column is not greatly disturbed in terms of its density distribution by evaporation. The amount of evaporation is sufficient to maintain the current environmental lapse rate, no more. Most of the latent heat is released as thermal energy, and eventually radiated away to space. But on days with exceptional humidity and heat, more of the latent heat release goes into PdV work, which pushes air up and reshapes the overall density profile.

Again, if I am reading correctly, William and I are making the same criticism on the same basic point: the GCM’s are not set up to track or even recognize the work done by rising air packets. My paper focuses on the long-term density shift over decades that must occur due to net warming. His paper focuses on the daily cycle of precipitation. But we wind up at the same conclusions, that water vapor feedback is negative and that the positive water vapor feedback seen in GCM’s is an artifact of poor model design.

We also seem to agree that Ferenc Miskolczi’s work is highly relevant. I’m very keen to see if this makes sense to William.

wayne says:
January 5, 2012 at 9:13 am
First answer my question, is there any way within a vertical column under gravitational pull, with a solid bottom, static, totally insulated, no energy going in or out, in equilibrium, it’s been standing there 10km high for a million years (hypothetical), are all molecules at the same mean velocity. Could they ever be different in that case?

Shouldn’t there be a heather in your hypothetic tube, to keep the bottom at our average 288K?
(or simulate a day/night temp. ritm)
This would cause the whole column to be “sorted” in the long run, with the warmest air at the bottom. When stable, the total energy (sum of thermal end potential energy) at each level should be equal.

“This would cause the whole column to be “sorted” in the long run, with the warmest air at the bottom. When stable, the total energy (sum of thermal end potential energy) at each level should be equal.”

Just sticking with the gravito-thermal anomaly question, I think that the Loschmidt paradox has been resolved. The question can be put thus. What is the temperature distribution in an adiabatically isolated gas column that is in thermal equilibrium. Is the temperature the same throughout the column, or is there a temperature gradient along the direction of the gravitational field? There are two conflicting answers to the question that creates the paradox.

(1) The temperature is the same throughout because the system is in equilibrium.
(2) The temperature decreases with height because energy conservation requires that every molecule loses kinetic energy as it travels vertically upwards, so the average kinetic energy of all molecules decreases with height and that the temperature is proportional to the average molecular kinetic energy.

Coombes and Laue (1985) and Velasco, Roman and White (1996) tackled this apparent paradox and showed that the correct answer is in fact (1) above. i.e. the temperature is constant throughout the column. I refer readers to these papers.

Qualitatively, since both the kinetic energy of the molecules and the number density of the molecules decreases with height, the average molecular kinetic energy does not necessarily decrease with height. The average molecular kinetic energy is the summation over all values of molecular energies divided by the number of molecules in any specific volume element. This average kinetic energy is constant throughout a column of gas in a gravitational field.

I refer the readers to these two papers for an elegant dissection of this problem:

Temperature (of gases at any rate) is really a compound metric for kinetic energy and number of molecules in a volume. Temperature is often used incorrectly as a synonym for energy. Perhaps if ‘temperature’ were to be abandoned as a metric then things would become clearer? What is interesting is the amount of energy in the volume which as others have said is greatly affected by enthalpy and the non-linear energy capacity of atmospheric water as it changes state. Ignoring these issues to simplify the mathematics appears to have led to gross miscalculations of atmospheric behavior in GCMs.

I note your argument:
“The average molecular kinetic energy is the summation over all values of molecular energies divided by the number of molecules in any specific volume element. This average kinetic energy is constant throughout a column of gas in a gravitational field.”
is a quote from the second paper. I’m not certain, but it looks to me like it sidesteps the issue this thread addresses by referring to the molecules outside the context of the volume they occupy.

Perhaps Hans Jelbring might be able to clarify, as if I haven’t given him enough work to do already. :)

Your second link is not to the paper Paul Dennis cited but rather to to a comment by (I guess) Roman, White, and Velasco. Actually, it is probably more relevant than the 1995 paper Dennis cites, but in the middle of it they plop several daunting equations full-fledged, like Athena from the head of Zeus. Presumably their 1995 paper shows how those equations were derived.

Do you by any chance have access to a (free-copy) link to the 1995 paper?

A layman, I’ve received different answers to the question, and they’ve all seemed plausible, although the temperature-gradient answer is the one that most appealed to my intuition–which, unfortunately, I have learned not to trust. What’s interesting here is that, unlike other treatments I’ve seen, the discussion that starts with Equation 5 of the Velasco et al. comment appears to have been derived from a statistical-mechanics point of view, which could give us laymen a better basis for judging which approach is right–if we could see its derivation, which presumably is in Roman et al.’s paywalled paper..

Sorry for the delay in responding but I wanted to read your “Pot Lid” paper first because I did not understand your assumptions concerning density in your comments. I still don’t. But I picked up a lot of information on the structure of GCM models that I was not aware of, especially their use of the hydrostatic equilibrium equations and their failure to combine several processes into one model. I did not realize that the GCM models did not allow for mass transfer between layers. And if they are relying on the hydrostatic equation, then temperature is not handled well since its basic assumptions include a constant temperature. I assume temperature is handled in another way?

Your summary of my paper is pretty accurate – a few minor quibbles but nothing important. Your reference to the missing tropical “hot spot” is on target. As I understand it, the reason it does not exist is that, in the tropics, a greater portion of the thermal energy released by latent heat condensation is converted to PV work and is not reflected as temperature. The result is a higher lapse rate than the models predict. (See my paper). The latent heat and air mass are transferred to much higher altitudes than the models predict. Based on discussions with the late Noor van Andel, I learned that the GCM models assume a constant equivalent potential temperature from the surface to the tropopause. But in fact, deep convection shows a declining EPT for the low to middle altitudes and a rising EPT thereafter. (The decline is due to the existence of PV work energy in lieu of thermal energy). The maximum convection height occurs where the EPT at altitude equals the surface EPT. I have confirmed that relationship with the radiosonde data that I used for my E&E paper. Would you know if the constant EPT is truly contained in the models? That would be a very fundamental mistake if it is true.

Yes, I agree that the work of Miskoczi is very relevant. I have had discussions with him on a few occasions. We both agreed (I think) that understanding the non-radiative processes, his variable “K”, are key to making his empirical model come together.

May I propose a “thought experiment” ? What would happen to the Earth’s climate / lapse rate if the atmosphere were to be instantly replaced with one of the same mass (of any chemical mixture) but which did not contain water?

I think (but I am not certain) that I know the answer, however I would like to know what otheres think.

James Hansen once said that water vapor and CO2 are jointly responsible for most of the 33 K difference between the “airless rock” temperature of 255 K that is commonly cited, and the Earth’s average sea level temp of 288 K. That is, the Earth is warmer by at least 7 to 12 K, and perhaps more, because it has oceans.

There is a serious problem with that — and laying the problem out may help me in explaining my density argument to William.

Suppose that the Earth has dry air containing CO2 and methane and whatnot, and some average surface temperature T0. The lapse rate is about 10 K/km. Now suppose that we add water vapor. According to the standard model, the atmosphere becomes far denser and blocks escaping longwave radiation, and then “back radiation” causes the Earth to heat, until a new equilibrium is reached at some new and higher temp T1. I have no objection to this part of the standard model. Hansen’s estimate of 7 to 12 K may well be correct; when I do the optical density calculation and try to work out the new radiation balances, I get a number in this range.

But the lapse rate also drops. So supposing the tropopause was 13 km up, the new temperature up there is not going to be T1 – 13*10 K, reflecting the dry lapse rate. It is going to be T1-13*6.5 K, which means that while sea level rises by (T1-T0), the temperature at the tropopause is going to rise by (T1-T0)+13*3.5, or about 45.5 K more than at sea level. In percentage terms, it’s a huge difference.

Now, here is the really head-scratching part. Miskolczi has alluded to this point, and it is vital to any understanding of climate change. If the sea level temperature rises to T1, then density there must fall to T0/T1 of its original value. That is because the surface pressure is fixed by the weight of the atmosphere. It is a boundary condition that never changes. The wet air, being hotter, would then be less dense at sea level than dry air. If T1-T0 = 12 K, the difference would be about 4 percent.

BUT if the temperature at the tropopause rises by the amount shown above, then the wet air up there is going to be less dense as well. Indeed, you will have the mother of all “hot spots” in the upper troposphere, because temps would rise far faster in percentage terms. Start with a dry tropopause temp of 125 K, then increase sea level by 20 K and tropopause by 65.5 K, and density falls by about a third up there.

Here is where some people lose the thread, so hang on tightly. The density profile of the atmosphere CANNOT change in total area. There is a fixed amount of air. So if density goes down somewhere, it must go up somewhere else. It is mathematically impossible for the atmosphere to be less dense at sea level, and less dense at the tropopause, at the same time.

Hansen doesn’t consider this because the hydrostatic models do not allow the air to move. Each layer in the model (there might be 20, or 50, or whatever) simply gets hotter and thinner. So his account seems plausible to him, and to his colleagues at the dozen or so modeling groups around the world.

However, if you just play around with the ideal gas law and the International Standard Atmosphere, it is readily apparent that you cannot increase sea level temp AND decrease lapse rate at the same time. Combining these moves is energetically and mathematically impossible. Instead we have to assume that increasing the lapse rate will cause air to shift down to sea level, and the rising density at sea level (given the fixed boundary condition) will cause sea level temps to fall. That is the only physically possible state that the system can evolve to.

So I postulate a second step in the estimating procedure, after we have accounted for “back radiation,” in which air is forced down from higher up, and drives down sea level temps to T2. This is a negative feedback. T2 is less than T1. I contend that it’s actually less than T0, but that’s a subject for a much longer discussion. We want to focus on the essential points for now.

Some details of the way I explain this differ from William’s. Don’t let that bother you, because at this point we’re dealing with two related but separate questions. The key point is that William says you can’t heat the atmosphere AND decrease the lapse rate at the same time, to which I emphatically and wholeheartedly agree. That is quite sufficient to bring the IPCC model crashing to the ground.

My argument rests on comparing an initial state and an end state, across decades of gradual warming, and showing that the end state forecast by the IPCC models is impossible to reach without first isolating the layers. His rests on a calculation showing that massive amounts of energy from latent heat are going into lifting the air, not heating it. But of course if the modeled layers are effectively isolated from one another, the models won’t reflect that energy cost, the air won’t get lifted, and the forecast will be wrong — so we are making the same criticism.

I’m getting quite excited now. I think William’s argument, and mine, and Miskolczi’s, may turn out to be like the three legs of a stool. One deals with radiation balances; one deals with the daily dynamics of lapse rate change; one deals with the long-term density state function. They form a self-consistent picture that explains the failure to observe a “hot spot,” the decade-long pause in warming, the low RH values in the upper troposphere . . .

About EPT, I hesitate to generalize about how all models handle the details, because I’ve observed that they do differ in small ways, and because they don’t necessarily disclose everything. But I think that’s right.

To be clear, you’re referring to this formula for EPT:

theta = T * (P0/Pi)^(R/Cp), where R is the gas constant, Cp is heat capacity, Pi is local pressure for layer i, and P0 is sea level pressure.

In that case, yes, it seems pretty clear that if you use constant-pressure surfaces to define your layers, and the only transfer of mass between layers is a trivial circulation that more or less cancels out, Pi will be more or less constant in each layer, and consequently when the temperature Ti is converted to an equivalent potential temperature by reference back to P0, the ratio will be constant.

Real movement of air from lower layers to higher ones would cause Pi in the lower layers to be a larger value (more air piled on top of that surface). So the EPT in the lower layers would be depressed. But then the very top of the troposphere ought to cool a little, pulling air down from the stratosphere, reducing the total mass piled above a given surface, and thus the EPT as we near the tropopause should be increased.

The density shift should have those effects, and since there isn’t one, the effects are absent in the models.

I tried to hang on tightly, but, as you predicted, I lost the thread. Specifically, I was with you up through “The density profile of the atmosphere CANNOT change in total area. There is a fixed amount of air,” but I couldn’t get to ” if density goes down somewhere, it must go up somewhere else.” Couldn’t the tropopause and top of the atmosphere rise so that the density profile gets narrower everywhere but also gets longer so as to retain the same area?

Many thanks for your work on this. I think that I agree with your overall conclusion, but not exactly with your explanation, however, I will need to read this again (probably several times!).

If the dry atmosphere of the same mass (nitrogen, inert gasses, whatever) contained no CO2 would you come to the same conclusion, assuming the atmosphere to be well mixed by rotation? In other words are we looking at a pressure dominated effect?

i) The Greenhouse Effect however caused results from a slowing down in the transmission of solar energy into the Earth system, through the system and out again to space.

ii) Due to that slowing down more energy accumulates within the system which heats up.

iii) The process is exactly the same whether the slowdown is caused by gravity or by GHGs. One cannot argue that one is a breach of the Laws of Thermodynamics and the other not. Either both are or neither are.

iv) The gravitational effect involves every atom and molecule in the system including Oxygen and Nitrogen. It is too powerful for the non radiative processes such as conduction, convection and evaporation to negate it so radiative processes have to finish the job.

v) Thus the gravitational effect sets up the baseline lapse rate which is set as an inviolable minimum.

vi) The GHGs add another influence on top of the gravitational effect but it is the same effect in principle. However it is limited to the atmosphere and involves only a miniscule fraction of total mass.

vii) The thermal effect of those GHGs is to add energy to the atmosphere alone andt it does seek to increase the lapse rate over and above that set by gravity and pressure.

viii) Due to the GHG effect being limited to the air and being proportionately tiny compared to the gravitational effect the non radiative processes have little difficulty dealing with it and the vertical temperature profile of the atmosphere changes to on average and overall restore the baseline lapse rate set by gravity.

ix) Thus the radiative component of the greenhouse effect caused by GHGs is neutralised .

x) The climate consequence is a shift in the surface pressure distribution which has to occur in order to accommodate the change in the vertical temperature profile of the atmosphere but it is miniscule compared to natural variations caused by sun and oceans.

“…….Suppose that the Earth has dry air containing CO2 and methane and whatnot, and some average surface temperature T0. The lapse rate is about 10 K/km. Now suppose that we add water vapor. According to the standard model, the atmosphere becomes far denser and blocks escaping longwave radiation, and then “back radiation” causes the Earth to heat, until a new equilibrium is reached at some new and higher temp T1……..”

My understanding of the gas laws are that adding water vapor would not make the atmosphere ‘far denser’. The number of molecules of gas in a given volume at a given temperature and pressure is a constant – (Avogadro). As the molecular weight of H2O is less than N2, O2, CO2 then adding water vapor even without changing the temperature results in a lighter volume of air and convection.

The slab ‘hydrostatic’ layer models cannot cope with any convective effects and ignore the gas laws in favor of radiation. Thinking about it, this is what creates the modeled ‘atmospheric green house': they are replacing the green house glass with a mathematical simplification which stops their modeled atmosphere convecting in the same way as a sheet of glass.

Addition of water creates a very active atmosphere as energized H2O is quite “lighter” then O2&N2. But this is only effective between evaporation and condensation, so we have a Troposphere under a Stratosphere. A convective refrigeration system under a stratified radiation setup. pg

“Another very interesting discussion of the Loschmidt effect is given at this website:..”

Which leads to a real world pragmatic article starting “This was really driving me nuts.” and ends with the reason why I am a little puzzled. A planet with atmosphere is one thing but we are dealing with the real world where there is a bathing thermal flux, is highly dynamic.

Wind things back, as I roughly indicated 25th Dec the Marov paper about Venus shows both the radiative (aphysical) and found lapse rate (physical), together with garble I assume came from Sagan. I suspect Marov was a little tongue in cheek.
The point is that pure radiative cannot be, so trying to figure out the physics is a swamp.

Perhaps the case of an internally heated planet with _no_ sun is another limit case.

Divide and conquer as the heuristic might be useful, figure out all the pure limit cases first.

Having posed the question – what would happen if the atmosphere of the Earth was instantly replaced by an inert one of the same mass and volume? (say Nitrogen and an inert gas) – I believe I should give an answer: all else being equal, the enthalpy of the atmosphere would not change.

(I am surprised that nobody in this discussion refers to enthalpy)

But I have been known to be wrong before, and I will now run for cover………

Roger Longstaff says:
January 7, 2012 at 4:30 pm
Having posed the question – what would happen if the atmosphere of the Earth was instantly replaced by an inert one of the same mass and volume? (say Nitrogen and an inert gas) – I believe I should give an answer: all else being equal, the enthalpy of the atmosphere would not change.

(I am surprised that nobody in this discussion refers to enthalpy)

But I have been known to be wrong before, and I will now run for cover………

The entire AGW claim is based on global warming due to imbalance in the Earth’s ‘energy budget’ caused by ‘green house gases’ ‘trapping’ heat. Yet the evidence for the trapping of heat is claimed to be a rise in ‘average atmospheric temperatures‘. Yet due to the varying mixing ratio of water vapor the enthalpy of the Earth’s atmosphere varies considerably and temperature does not equal heat content nor even necessarily change in correlation with heat content..

To use the example from the WUWT post:

keep repeating the enthalpy argument back to people who can only talk in atmospheric temperatures

As I posted in the ‘Big Picture’ thread:

“Let us take a cool humid afternoon in Louisiana after a rainstorm has just stopped and the air temperature is a relatively cool 25C (77F) but the humidity is close to 100% at the same time in the Arizona desert after several weeks of drought the temperature is a really hot 38C (100F) but the air is almost zero humidity. It may come as a surprise to some that the 25C atmosphere in Louisiana holds twice the energy 76.9KJ/Kg, as the dry 38C atmosphere in Arizona 38.3KJ/Kg . If there are actually droplets of water for example a post shower mist in the Bayou then the energy content of the 25C Louisiana atmosphere is considerably greater. This is due to the enthalpy difference between saturated and dry air.

Yet ‘climate scientists’ proceed to average atmospheric minimum dawn temperatures with high humidity with afternoon temperatures with low humidity demonstrating a breathtaking ignorance of basic atmospheric physics and meteorology. What I have no understood is why they are not asked the simple questions on enthalpy that you raise. Instead, everyone clusters under the temperature lamppost and have detailed discussions of the statistical methods used in measuring the incorrect metric.

Without knowing the enthalpy of the atmosphere, temperature is of little guide to heat content. Water vapor, droplets and crystals have a huge effect on enthalpy and atmospheric density and they are ignored in the climate science maths. Its so much easier to use the maths of radiative physics and talk of temperatures and hohlraum radiation through an atmosphere of static slabs.

“The density profile of the atmosphere CANNOT change in total area. There is a fixed amount of air. So if density goes down somewhere, it must go up somewhere else. It is mathematically impossible for the atmosphere to be less dense at sea level, and less dense at the tropopause, at the same time.”

I am confused by your use of the term “area”. I have to assume you mean “volume”. Am I correct? Total atmospheric mass is a constant and pressure at any height is a constant but volume is not a constant. If the atmosphere increases in temperature at any point, the volume must increase. Thus the total atmosphere can increase in volume everywhere, there is no volume constraint. If the total atmosphere expands, the resulting temperature will be cooler (this is very pronounced in the tropics). I think this is an area where the models run into problems.

You also say,

“The key point is that William says you can’t heat the atmosphere AND decrease the lapse rate at the same time, to which I emphatically and wholeheartedly agree”

Correction, I did not say that you can’t heat the atmosphere and decrease the lapse rate at the same time. I’m sorry if I confused you on that point. I said that the lapse rate decrease can be less than that predicted by latent heat release alone. The degree to which the lapse rate will decrease depends on the PV work/thermal energy ratio that results from the release of latent heat. The higher the water vapor content, the higher the PV work/thermal energy ratio will be (which will determine how much the lapse rate will decrease).

But we agree that the “hot spot” seems to be a flaw built into the models, but we may disagree as to why.

Many thinks for obtaining that paper. For me it’s a little difficult, but I’m optimistic that once I’ve slogged though it I’ll conclude it has the final answer.

Hans had given me one good explanation already, and then he improved upon it in a comment to someone else in which he said that the adiabatic lapse rate maximizes entropy. Presumably the paper will prove that.

Joe, you are welcome. I’m happy to play librarian here, since my post crash brain refuses to handle complex algebra. Not that I ever was a whizz at it. I managed to get through my Polytechnic level V resit OK, but it was always a task for me. :)

If anyone using the info I’ve provided manages to do something elegant on paper,, I’d appreciate a digital photo of it to post along with their description of what is going on.

You state: “the adiabatic lapse rate maximizes entropy” – would you agree that this leads to themodynamic equilibrium? I think that this may be related to my constant enthalpy speculation, discussed above.

Actually, Hans was the one who said that. I do think it implies thermodynamic equilibrium, but don”t go by me; I’m just a retired lawyer muddling through this stuff in an attempt separate the climate-science wheat from the chaff.

Reading Coombes and Laue, I find the same problems cited in the letter by Velasco, Roman and White, particularly that the variables v and z are not statistically independent. That assumption actually forces the answer to come out as being a uniform temperature.

Coombes and Laue item (2b) is:

(b) Temperature is proportional to the average molecular kinetic energy.

Velasco, Roman and White wrote:

In conclusion, in our opinion a full explanation about why answer (2) to the paradox formulated by Coombes and Laue is wrong must discern between the cases of a finite system and an infinite system. In the former case, statement (2) is wrong because the assumption in statement (2b) is wrong.

The reason for this is in VRW equation 8 for a 3 dimensional ideal gas:
K(z) = 3*E*(1-mgz/N)/(5N-2)

VRW continue:

i.e., for a finite adiabatically enclosed ideal gas in a gravitational field the average molecular kinetic energy decreases with height.

I believe they misunderstood the poorly phrased item 2b. A better phrasing would be Temperature at any particular z is proportional to the average molecular kinetic energy at that z, which is no longer false.

As phrased by Coombes and Laue, however, it is false because the temperature is not proportional to the average molecular kinetic energy by itself.

Q. Daniels: thank you for your analysis. I haven’t had the time to study the papers, nor am I as able as I once was, so forgive me if this is a stupid question:

Is it possible that Coombes and Laue 2b is correct but incomplete insofar as it doesn’t deal with the limiting cases at either end of the column? i.e. the average at the centre of the column will indeed be the average over the whole column, but Coombes and Laue incorrectly extrapolate to a uniform T over the whole column later in their analysis?

“Couldn’t the tropopause and top of the atmosphere rise so that the density profile gets narrower everywhere but also gets longer so as to retain the same area?”

Nope. It’s a basic theorem from calculus, used in limits. Picture the original density-versus-height curve. At sea level it has a value of 1.2 kg/m3, and it falls to something like 0.25 kg/m3 at the tropopause, and keeps falling as we go up into the stratosphere. Atmospheric profiles like these are all monotone and asymptotic, but that’s not essential to the argument. Now picture a new density curve drawn somewhere inside that space, never crossing the line formed by the original one, always lower in value. In such a case, the original density curve MUST contain more total volume. The atmosphere can be stretched out as you describe, but for the two volumes to be equal, the new curve must cross the old one at some point, and be larger over some portion of the air column.

William:

“I am confused by your use of the term “area”. I have to assume you mean “volume”. Am I correct?”

I meant area under the density-versus-height curve. There’s a graph at the start of the “Pot Lid” essay that shows a typical density-versus-height profile. The total area under that curve has to be constant, per my explanation to Joe above.

Regarding lapse rate — hmm, okay, I think I see what you’re saying. The GCM’s show the atmosphere temps rising by 1.4 times the amount that sea level air does, thus a “hot spot”. The observed amount of rise is just 0.8 times as much. You’re not prepared to say that it can’t be greater than 1.0, just that it is less than 1.4. Fair enough.

Roger:

“If the dry atmosphere of the same mass (nitrogen, inert gasses, whatever) contained no CO2 would you come to the same conclusion, assuming the atmosphere to be well mixed by rotation? In other words are we looking at a pressure dominated effect?”

No, sorry, I slipped up a little bit. In my post I switched between talking about air density to OPTICAL density. Ian W. spotted this slip as well. By “density” in that context I mean the percentage of longwave radiation that the atmosphere intercepts. A dry atmosphere with just CO2 has a relatively low optical density, something like 0.18, while our current wet atmosphere has an optical density of 0.83 or 0.84. So adding water increases the optical density by about 0.65 or 0.66. It does increase the air density by a small amount but that is not the point I was trying to make.

I use the term “optical density” a sentence or two later, and it made sense to me when I reread it, but I needed to stop and say that I was changing to a different meaning of the word. Sorry.

Coombes and Laue (2b) is poorly phrased, with the literal reading being opposite the contextual reading. The contextual reading includes the omitted words “at any particular z”, which produces very different results.

It seems to me that Velasco, Roman and White were addressing the literal reading, which I take as actually being equivalent to Coombes and Laue (1).

Unfortunately, that’s the best I can do for untangling that particular piece of spaghetti logic.

The more serious mistake is assuming that z and v are independent variables after specifically working out their relationship. If you assume they’re independent, then you’re actually assuming that velocity (and thereby temperature) does not vary with altitude. I can’t help that one.

Q.D.: Thanks for the further analysis. It seems that my intuition that there was something wrong with Coombes and Laue’s paper was correct then. I’m grateful for your technical confirmation of that. I wonder which other papers ‘falsifying’ Loschmidt will pop out of the woodwork as the threat Jelbring and Nikolov and Zeller pose to the orthodox interpretation of atmospheric thermal organisation becomes more widely recognized. :)

For decades I was well served by following the theory that in the search for truth there are no stupid questions. But I see in retrospect that my question to you above may be a counterexample, so I am particularly grateful to you for having the patience to respond.

I have now downloaded your paper, to which I will turn for relief during periods of frustration in attempting to understand Roman, White, and Velasco’s paper.

1. We have a planet in outer space, sufficiently far from any stars, so it only “feels” the isotropic thermal radiative filed of CMBR, temperature 2.725 K.
2. Its surface is covered by an extremely black material (like a deep layer of fluffy soot or something), making it a perfect black body along the entire EM spectrum.
3. Volume & mass of the planet matches that of Earth, but it does not rotate, so it is a perfect sphere.
4. Surface temperature is kept at a uniform and constant 288 K by a steady internal heat source (put an appropriate amount of some long half life radioactive isotope inside, ⁴⁰K perhaps).
5. Surround it with an atmosphere of an inert diatomic gas like N₂ which has no absorption line whatsoever in the thermal infrared (that is, it’s not a greenhouse gas, it is transparent, it neither absorbs nor emits IR), set surface pressure to 1 atm.

Question: What is the equilibrium distribution of pressure & temperature in its atmosphere as a function of height above its surface (let’s say after a relaxation time of a million year or so)?

Your gedankenexperiment is similar to my thought experiment (see above), but it isolates the essential physics more explicitly. (I would have suggested an atmosphere of Nitrogen and Neon, in order to match mass and volume). Nobody wanted to play with mine, so I will play with yours – enthalpy and lapse rates (t&p) same as Earth.

Roderich W. Graeff is a crackpot. There is actually an upward negative temperature gradient in a closed system in thermodynamic equilibrium, resting in a gravitational field of strength g(due to gravitational redshift), so Loschmidt was right in a sense, but it is many orders of magnitude smaller than Graeff reckons. The exact formula for this gradient is -gT/c² (which is about -3.27×10⁻¹⁴ K/m at 300 K).

This gradient should be independent of the internal construction of the closed system, otherwise a perpetuum mobile of the second kind would be possible (I can see Graeff has his own Gravity Machine… even sells a book on it). But the second law of thermodynamics is somewhat more general, than any specific physical theory.

However, the atmosphere is not a closed system, it is not in thermodynamic equilibrium, not even close. It is in a (more or less) steady state, but that’s something entirely different.

While I agree that plans for a free energy source built on the back of Loschmidt’s hypothesis are probably wishful thinking, I don’t think we should dismiss Loschmidt on the strength of Graeff’s alleged crackpottery.

He has performed some reasonably well documented experiments and the results are the results. Seems to me that the best test is attempted replication; preferably by a high quality independently resourced lab.

It may turn out that Graeff’s most important contribution is his reformulation of the second law. It may or may not turn out that his stipulation that energy fields which penetrate the postulated energetically isentropic closed column must be removed or accounted for is unnecessary or redundant. Either way, it gets us to the nub of the issue.

We are discussing all testable objections to Loschmidt’s hypothesis in this thread, such as the Coombes and Laue paper discussed above. That was found to contain unsupported (so far as we know) assumptions which determined their result.

So as far as I can see, since Boltzmann didn’t succeed with his attempted disproofs and Maxwell relied on assertion, the question is still open.

We all accept that the ‘gravitational redshift’ is a tiny effect we can disregard here.

Am I correct in stating the surface itself is free, doesn’t matter what it is? (a side effect of having magical heating)

The item which worries me is gas perfection where I was not aware of any real gas with zero radiative properties. Is that true?

Tim, I don’t understand your first question.

The second one is interesting. It is said that nitrogen for example has an absorption spectrum which is orders of magnitude smaller than co2. But then, there is orders of magnitude more nitrogen in the atmosphere than co2…

Rog,
The planet/body has an internal heat source generating whatever heat is necessary to maintain a constant surface temperature.
Heat interchange with the gas is by conduction only a corollary of the radiation free gas.
In consequence the emissivity properties of the actual surface do not matter. Q: is that agreed?

We need to be more careful to differentiate between surface temperature, and near surface air temperature.

However, as far as I know. The variation in surface temperature is more strongly affected by the near surface air temperature and incident solar radiation than it is by the heat in Earth’s core, due to miles thick insulation provided by the crust. I hear the radiation due to internal heat escaping is measured in milliwatts, on land at least.

As the majority of the heat energy from the surface of the Earth is transported to the tropospause by convection of moist air and not by radiation, is this thought experiment useful? Or is this a cluster under a lamppost where the maths is easier? ;-)

Ian, the point of the experiment, if I understand it correctly, is to extract the basic physical principle that the laws of thermodynamics, gravity and the gas laws subsume all internal energy transfer mechanisms such as radiation, conduction and convection (please correct me if I am wrong). In a well mixed atmosphere it is only the mass of the atmosphere and gravity that matter in a steady state.

“Is not it simple high school physics?” as the questioner states. The answer, however, has a profound effect on the current debate (in my opinion).

At no place in the troposphere is there no water vapor. Over ocean or desert there is some amount of water vapor present. Water vapor with energy, swamp any gravity effects on the apparent temperature of the air near the earths surface. Until you reach the altitude that the air is freeze dried, the effects of moisture is the driver. The troposphere is a very different animal to that of the stratosphere. It is not high school physics or we would not be having this discussion. Water vapor is the most important gas in the cause and effect of weather/climate or we would not have a troposphere. pg

As to the the simple high-school physics, has anyone put numbers to Equation 6 in Velasco et al.’s critique of Coombes & Laue’s finding that temperature is uniform in an isolated column of air at equilibrium?

If I read it correctly, that equation is supposed to tell what the relationship would be between temperature and altitude at equilibrium, saying that temperature decreases as altitude. increases. When I put numbers in it, though, I get negligible variation. Did anybody else get that kind of result?

The power of convection in the atmosphere driven by simple fluid convection, by energy from water changing state (and volume) is huge. A single hurricane in one day uses 200 times the human worldwide energy generation capacity just due to state change of water while using only half the amount of human worldwide energy generation creating the winds.
( http://www.aoml.noaa.gov/hrd/tcfaq/D7.html )

Every weather system in the world is similarly continually using/transporting huge amounts of energy. Assuming the effects of water and the complex fluid dynamics caused by convection accelerated by water are not present is discarding probably 90% of the problem.

I’m going to make a final comment here for after reading all of the above comment, most very good and enlightening, no one seems to see this as I do. I have spend a great amount of time, multiple of thousands of hours dealing with gravity at the solar system scale in the last ten years and I can vividly see a decouple of the laws governing gravitation and thermodynamics, the later not being one of my heavy suits.

Let me see if I can draw a mental picture of the way I see where they are not connected.

Take a perfect cube, one meter on a side, vacuum inside with one lone molecule. Align the sides of that cube so all sides are parallel to the xyz axises. If that molecule has a velocity exactly parallel to one of the axises, it will bounce between the two perpendicular side FOREVER creating pressure. That is an assumption that all of the thermodynamics equations are built upon. All paths of the molecules travel in a perfectly straight line.

Now put that cube in a gravitational field, like sitting it on the ground and aligning the sides to those three xyz axises again. That lone molecule traveling perfectly parallel to the z axis will also bounce up and down between the top and bottom sides, never wandering in the xy direction FOREVER creating pressure. But there is a difference. It will slow as it moves upward or speed up when moving downward causing more pressure on the bottom than on the top creating a pressure differential between the top surface than the bottom. I think all above understand that and have a clear view of that aspect.

But what I don’t see everyone also playing into this discussion is what happens when that molecule is traveling precisely parallel to one of either x or y axises. A molecule does not realize where it ‘is’ in space. It’s path is no different than a satellite, it’s curved. Tiny I realize but curved downward toward the center of the body creating the gravitational field never the less. So when it travels across the cube and hits the opposite side it will hit very, very slightly lower z than where it would in the gravity-less example. And it will hit at an angle. As that molecule bounces between the two walls that angle will grow and grow with even transit across the cube and if the we now envision that as a very tall column instead of having a volume of just one cubic meter, the molecule which started near the top will have a sizeable vertical component when it gets to the bottom. How much of a vertical component would depend of course on both it’s velocity and the amount of gravity present. That vertical component ALSO creates an even greater pressure at the bottom than the top. Even horizontal creates movement creates more pressure at the bottom. To me that seems to be the culprit.

Thermodynamics, unless I am mistaken, does not seem to address BOTH of these factors created by a gravitational field and it is the horizontal assumption of straight paths that may be the missing factor that Loschmidt also saw in his mind. We will never know I guess.

Well, that’s the way I tend to approach that decouple between those two branches of science. We may very well need a modified second law of thermodynamics to account for this in very extended space (xyz) cases in a gravity well. Our atmosphere sure seems to fit that case.

Q. Daniels, that’s a goof way to put it, ballistic trajectory, I’ll use it. A few non-science oriented persons I tried to describe this to yesterday had a problem equating satellite orbits with molecular paths. Yours is much more intuitive. Thanks.

PV + (1/2)mv^2 + mgh = constant : where V is the volume of the fluid and P, density of the mass constant over the entire volume

PV is an energy term

but it’s more generally

P + (1/2)ρv^2 + ρgh = constant : where ρ is the local density of the fluid
This equation is true at every single point. Integrate the Bernoulli equation over a volume V and you get the first equation.

I assume ‘v’ is the rms velocity. This is the first time I have seen (or just lost in the fog of time) relating pressure and density mixed into thermal kinetic energy and potential energy as the total energy at any point in a system. Hmm.

Your single-molecule thought experiment is valid, but, unless I’m mistaken–as I frequently am– the papers that tallbloke has graciously obtained for us establish that temperature at equilibrium is essentially independent of altitude for any reasonably large number of molecules.

Now, Equation 8 of Velasco et al.’s critique of Coombes & Laue states that temperature does indeed decrease with an increase in altitude, so it is consistent with your thought experiment. But, if I read that equation correctly, the decrease it specifies is negligible until you reach an altitude in the gas column where a single molecule’s potential energy is a significant fraction of the total energy content of all the molecules. That condition prevails in your thought experiment, which assumes only a single molecule. But, unless the altitude greatly exceeds that of the top of the atmosphere, that condition would not prevail even with as few as 10^9 molecules–which in our atmospheric-pressure regime would require the gas column to be so narrow that a molecule would barely fit..

But Velasco et al. is based on Roman et al. (also provided us by tallbloke), which arrived at its conclusion through the statistical-mechanics technique of, for each combination of altitude and velocity, counting up all the (equally probable) microstates that are consistent with that combination. This is the approach that strikes me as most reliable.

Still, I can’t profess to have followed all Roman et al.’s logic completely. (E.g., they rely on the identity expressed in their Equation 5 but derived in another pay-walled paper. For that matter, I haven’t even attempted to verify the integration in Velasco et al.’s Equation 8.). But the most compelling way for the experts to demonstrate (as I’m sure they could) that the equilibrium lapse rate is what they say would be to show either where Velasco et al. are wrong or (more likely) how I incorrectly interpreted their Equation 8.

Hi Joe. Your right, that idealistic example would never really occur in nature, just presented for someone to visually see the point of the process and then think how that same effect would occur in mass with a count of molecules with about 29 zeros behind it. But really, since molecules in our atmosphere are actually space quite far apart, about 1000 times the molecules diameter I read, for a split moments between collisions they are just moving in space and they do accelerate, decelerate and curve just as that one molecule example in a gravitational field. That is what I was trying to get across, just physical clarification.

Even though I definitely feel a machine on such an effect would be impossible for total energy would be equal at both the top and bottom, I’m still trying to digest the math for something seems to not quite jell, and it should, for I do think that effect is real.

A good thought experiment, To add, a molecule would be a perfect elastic. If it hits the base harder, under gravity, then it will rebound higher into the column. Em, sounds like added energy to me. Energy that is pulled towards the bottom. pg

Just to be clear, my interpretation of Velasco et al.’s Equation 8 is indeed consistent with the effect you describe; it’s just that–if I’m interpreting it correctly–that equation says that for large numbers of molecules your effect results in a negligible lapse rate. This is contrary to what all the experts are telling me. Since statistical mechanics is to my way of thinking the closest thing to arguing from first principles, though, it would be great if we could get to their conclusion by a statistical-mechanics approach similar to those papers’.

I.e., I’m hoping someone will show me where I’m wrong.

One of the things that gives me pause, by the way, is that Levasco’s Equation 6, which I interpret as density, gives me a density drop of the type our atmosphere exhibits only if the singular-molecule potential energy mgz is on the order of 1/100 the total system air-column energy E, a value that’s orders of magnitude too large.

Well I’m not up to assessing all the equations so let’s look at the concepts.

The atmosphere troposphere clearly has a lapse rate with temperature declining with height. There are variations such as the stratosphere but overall from top to bottom the lapse rate is such as to ensure that the surface is at a temperature that at equilibrium radiates energy out at the same rate that energy arrives from the sun.

I’ve always understood since school days long ago that the lapse rate is induced by atmospheric pressure and is therefore a consequence of the planet’s gravity which is derived from the planet’s mass plus the mass of the atmosphere.

AGW theory proposes that in fact the lapse rate is a consequence of radiative processes from GHGs causing the surface to be hotter than it otherwise would be.

Thus it was proposed that the best way to demonstrate the gravitational/pressure idea would be to use an isolated container as proposed above to see whether under gravitational influences alone the bottom of the column became warmer than the top i.e. the lapse rate was duplicated within the column without any radiative influences from GHGs.

There seem to be no conclusive experiments that resolve the issue though Graeff claims to have achieved it. No verification as yet though. The main problem would appear to me to be the creation of a sufficiently tall and sufficiently isolated column. Those two requirements are most likely incompatible in practical terms.

Pending a definitive experimental demonstration we are left with the Ideal Gas Law which has a provenance of more than 100 years but which deals with the issue perfectly well and I’m pretty sure that in my schooldays that was regarded as sound enough to explain the phenomenon of an atmospheric lapse rate.

It makes sense because a denser air mass with more molecules bouncing around at lower levels is the natural consequence of a downward gravitational pull and more bouncing around of molecules in a denser atmosphere surely slows down the upward transfer of energy to space.

Against that we have the more recent AGW idea that the surface is only warmer than the top of the atmosphere because of GHGs. There is some historical support for the proposition that GHGs process radiative energy more effectively than do non GHGs such as Oxygen and Nitrogen but I have not seen a clear demonstration that the outcome is necessarily a warming of the entire Earth system as opposed to localised atmospheric warming that is readily removed by faster non radiative processes.

GHGs radiate 50% of their energy upward and I have seen no evidence that the portion radiated downward does anything more than balance out the energy lost upward for a zero net effect overall.

I think both types of greenhouse effect exist and their effects need to be separated out and put in proportion to each other.

I don’t see it as plausible to deny the well established Ideal Gas Law as relevant to the presence and scale of the observed lapse rate and to throw out its implications in favour of an assumed rather than proven radiative theory.
[edit, from email — Tim]

PG, yeah, I was assuming perfectly elastic collisions. But, my little mental physics simulation (so far, may numerically integrate it later) tends to show that the molecule would end up over time returning exactly back to where it began, high in the column and, get this, I think, perfectly horizontal once again, all energy perfectly conserved. What I’m saying is I can’t see it returning to a higher point after a number of iterations. So much for simplistic examples.

Joe, since I’ve had some r&r (sleep) I do see where it just returns to the point in a real example where pressure and density will be higher when lower, and that PV energy coupled with the fact that gases are not perfectly ideal and you do have to allow for the volume of the molecules. And there are possible inter molecular force as van der Waals involved. These factor cause the density curve to not precisely follow the pressure curve and it seems to me right now that it is those factors making it warmer when lower in height and creating a real preferred lapse rate. Look at the pressure and density curves on any of the Standard Atmosphere graphs. They diverge, the P/rho ratio. I’m still investigating that factor.

One can sidestep a lot of the conceptual problems some here are having if one regards the density/mass/pressure of the atmosphere as shifting the balance (within the flow of energy through the system) from fast radiation towards slower conduction giving a rise
in equilibrium temperature as a consequence.

After all, no atmosphere at all means an immediate turnaround of energy i.e.
radiation straight in and straight out pretty much instantly.

As soon as one then adds an atmosphere capable of CONDUCTION which includes non GHGs then the
conduction takes away from the efficiency of the radiation process by
slowing energy dissipation down which is what then leads to the higher
equilibrium temperature. The denser the atmosphere the more conduction takes
place before the radiative energy can be released to space and the higher
the equilibrium temperature rises.The density of the atmosphere at the surface is controlled by gravity because a stronger gravitational pull reduces volume.

So, radiative processes are not in control because they are subject to
interference from density and the consequent increase in conduction relative to radiation.

Convection and the water cycle then act to try to reduce the slowing effect
on energy dissipation of more conduction but can never get back to the
efficiency of raw, in/out, radiation.

In order to maintain the outward radiation of 240 Wm2 and thereby match the incoming of 240Wm2 the surface temperature needs to rise in order to overcome the retention of energy by the atmosphere caused by conduction to the air.

At Earth’s atmospheric pressure the surface temperature rises to a point where the surface needs to radiate 390 Wm2 in order to get 240Wm2 out into space past the resistance of the atmosphere.That atmosphere absorbs via conduction the balance of 150Wm2.

That all happens as a result of atmospheric mass. Nothing to do with the thermal properties of GHGs so that then provides the baseline adiabatic lapse rate for our particular planet.

If one then adds some GHGs then they will have an effect but only above the surface and so far no one has suggested any evidence that the 50% of their emissions directed downwards to decelerate the energy flow through the system fails to be offset by the 50% that goes upward to accelerate energy flow out of the system.

Or that increased convection and evaporation fail to eliminate the contribution from GHGs.

So we have a clear and obvious greenhouse effect from atmospheric mass but no proven similar net effect from GHGs.

Steven, it seems you may be addressing me. And I know why. This is a real effect since it all comes down to ρT = constant as Nikolov & Zeller laid out in the first column of their poster. That simple. No speaking of single molecules needed and evidentially maybe not welcome. Mea culpa.

But I am rather new to thermodynamics, have sat through the MIT courses, twice, but there’s nothing like working with it for your life to get a real feeling for the equations which I lack. I probably shouldn’t comment on what is going through my mind at each moment, It may look more like a statement from me than a mere plea for others to help fill in the gaps. I do usually like to know the reason underlying the equations though, some say it is a flaw, some say it is gift.

Now on what you were laying out above on conduction, I see much in what you are saying. Let me tippy toe into it a step at a time.

Did you ever read many month’s ago where I was trying to get everyone to see that radiation if absorbed close to its source, that is its mean path length is small, is in all respects and in reality, just fast conduction? Conduction goes molecule to molecule at the speed of sound but radiation goes from molecule to molecule at the speed of light and travels much further depending on how thick the gases are at a given frequency.

I see that as a physical fact. Do you? Can you also mere radiation into your thoughts on conduction. It may help develop you thoughts for others.

I just see in the thick troposphere near the ground most ghg radiation at their perspective lines just bouncing a few (~5-150) meters from molecule to molecule and maintaining warmth near the surface, some (~23 Wm-2 per FT97) always making its way to space. That is saying, fast conduction, and that 23 Wm-2 is all I see LW radiation having to due with energy in the low atmosphere. Would that be stated right? Seems pretty parallel to what you are saying.

You may be interested in the concept that the lapse rate works to maximise entropy. The text below is taken from an abstract of a 2002 paper by Lorenz:

“Two thermodynamic principles offer considerable insight into the climatic and geological settings for life on other planets, namely (1) that natural systems tend to actually achieve the ideal (‘Carnot’) limit of conversion of heat into work and (2) if a fluid system such as an atmosphere has sufficient degrees of freedom, it will choose the degree of heat transport that maximizes the generation of work (equivalently, that which offers maximum entropy production). The first principle agrees well with results on terrestrial cumulus convection, and the mechanical energy released by tectonic activity. The second principle agrees with the observed zonal climates of Earth, Mars and Titan”

Wayne, it wasn’t directed to anyone in particular and I agree that there is a similarity between your comments and mine.

Certainly conduction and radiation operate at different speeds so simply altering their proportions would result in the observed real world outcome. I think it is best to keep them seperate so as to not blur the differences between AGW theory which says the atmosphere warms from downward radiation and mine which says the atmosphere warms from conduction moving up from the surface.

Roger Longstaff, two helpful thermodynamic principles that seem to firm up on the basics of what I said.

Just in case there’s still anyone out there attempting to reconcile what he thinks he knows about lapse rate with the papers tallbloke provided us, I’ll give a layman’s-eye view of what’s going on in Román et al. and Velasco et al., which relies on Román et al.

Román et al. deal with a vessel that is disposed in a gravitational field and contains N identical-mass monatomic molecules (i.e., molecules whose kinetic energy is all translational; none is manifested in tumbling or vibration). The vessel so isolates the molecules that their aggregate total (kinetic plus potential) energy E is constant. To arrive at the molecular-velocity (and therefore temperature) distribution as a function of height, the authors use a technique they characterize as “counting microstates.” Rather than count discrete states, though, they integrate through a continuous “phase space.” That is, since each molecule’s state can be completely described by its (three-dimensional) position and (three-dimensional) momentum, the total system state can be described by an ordered set of 6N scalars, and the system state at any instance can therefore be thought of as a position in a 6N-space, a “phase space.”

Their technique is based on the assumption, which I take it is well accepted in statistical mechanics, that the probability of the system state’s falling within any region of that phase space is proportional to the volume of that phase-space region. Now, the constraint that energy is fixed restricts the system to a (zero-volume) hyperparaboloid in that phase space, so the probability that the (energy-constrained) system will fall within a given range of states having that energy becomes the ratio of that range’s area on the hyperparaboloid to the total hyperparaboloid area. Equation 2 adumbrates this approach, giving a function that is zero at all places in the phase space except those that have an energy E, where its Dirac delta function gives it an infinite value that, when the function is integrated over the volume that contains the hyperparaboloid, yields unity
.
To find the position and momentum distribution for a single one of those molecules, Román et al.’s Equation 9 integrates all the other molecules’ positions and momenta out of that function and restates the result into a form that lends itself to use of a magical identity they introduced in Equation 5 as proved by a pay-walled paper. This is how they perform the integration that leads to their Equations 12, 14, and 15, which Velasco et al. adopt as their paper’s Equations 5, 6, and 7 for the distributions of molecular position and velocity.

It is from the thus-obtained Velasco et al. Equations 5 and 6 that they claim to obtain their Equation 8 for temperature as a function of altitude, and it is that equation that seems to me not to jibe with any significant lapse rate: although it does have temperature fall with altitude, the drop, if my calculations are correct, is negligible.

I have not read all of the papers, but are you referring to a Maxwell-Boltzman distribution of velocities, or something quite different?

From wiki:

“The Maxwell–Boltzmann distribution describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions. It describes the probability of a particle’s speed (the magnitude of its velocity vector) being near a given value as a function of the temperature of the system, the mass of the particle, and that speed value.”

I think it is best to keep them seperate so as to not blur the differences between AGW theory which says the atmosphere warms from downward radiation and mine which says the atmosphere warms from conduction moving up from the surface.

Stephen, I feel you’re right on target with your statement. What you don’t seem to consider is the effect of the oceans temperature, AND their ability to convert and store “excess” radiation to an average temeperature slightly above the assumed 288K average surface temperature.

The authors state that the expressions at which they arrive approach Maxwell-Boltzmann in the limit. See Román et al.’s discussions at the end of the last paragraph in their Section 1 and the beginning of their Section 3. (Actually, I hadn’t gotten to Section 3, since I was interested only in the part referred to by Velasco et al. in their critique of Coombes and Laue. Now that I’ve glanced at it, I realized that it may be helpful.)

Thanks for the links, skimmed through them, will read more carefully.
Hot Water Bottle Effect seems right on the money.
Only thing I try to stresss is the imo wrong calculation of the basic blackbody temp in the present CAGW theory. (255K)
If the earth was flat, facing the sun, following the same logic this temp would be 0,7 * 1364 = 955 W/m^2 SB > 360K !!
Spreading incoming radiation over the whole sphere (dividing by 4) and THEN calculating the blackbody temp is wrong, as also stated by Nikolov and Zeller.

I now see that my reading at least of Velasco’s Equation 6, relating density to altitude was faulty and that it now makes sense.

What I said above was:”One of the things that gives me pause, by the way, is that Levasco’s Equation 6, which I interpret as density, gives me a density drop of the type our atmosphere exhibits only if the singular-molecule potential energy mgz is on the order of 1/100 the total system air-column energy E, a value that’s orders of magnitude too large.”

What I failed to realize is that its (1 – mgz/E)^[(f/2 + 1) / N – 2)] approaches an exponential, so I didn’t have to make the above (it appears, erroneous) extrapolation from small-number numerical results. That expression is of the form (1 – x/a)^N, which approaches exp(-Nx/a) as N and a approach infinity so long as N/a is finite. For large values of the number of molecules N and (dimensioned) ratio E/mgz of total energy to single-molecule gravitational force, that is, Velasco’s Equation 6 expression for the gas density as a function of altitude becomes a value proportional to exp(-Nmgz/E) = exp(-mgz/E_m), where E_m is the mean molecular total energy. If we assume a reasonable density function that decays to 1/e atm. at 12,000 meters, mg/E_m = 1/12,000/m. This give a total (kinetic plus potential) energy E_m per molecule of equal to the average translational kinetic energy of a 410 K gas, which seems plausible.

Joe Born says:
“Still, I can’t profess to have followed all Roman et al.’s logic completely. (E.g., they rely on the identity expressed in their Equation 5 but derived in another pay-walled paper.”

Which paper Joe? I provided the paper containing the ‘Athenian’ calcs. Is there another i need to find? I’m really excited by this discussion, and I’m trying to stay out of it while you guys agree on some definite findings.

Fernandez-Pineda, Mengual, and Diez de los Rios 1979 Am.J. Phys. 47, 814-7. It’s cited as the basis for Equation 5 of what you’ve dubbed the Athenian Calculations and I’ve been referring to as Roman et al. paper.

However, although I personally would love to see that paper, it seems unlikely that the congnoscenti consider the Equation 5 identity controversial, and I sense that little interest remains among your readers in the statistical mechanics, so you may justifiably conclude that obtaining a copy of this paper isn’t worth your time.

Although I will be looking at the Roman et al. and Velasco et al. papers a little more, I believe I’ve just about arrived at the conclusion that their authors (and, in effect, Coombes and Laue) have all concluded that the equilibrium lapse rate imposed by gravity is negligible. It would be great if Hans Jelbring and William Gilbert could tell us where Velasco et al. are (or I am) wrong on the statistical mechanics, but I suspect that they would understandably consider it a waste of time to wade through the somewhat challenging equations just to prove to a single retired lawyer that the earth isn’t flat.

Even though I’ve yet to find the answer, I have greatly appreciated the learning opportunity this forum has presented–and I haven’t finished mining it: I’m just about to read Gilbert’s paper to remind myself how the equilibrium-lapse-rate proponents use traditional thermodynamics to prove their case.

By the way, one place I may have erred in attempting to comprehend Velasco et al. and Roman et al. is my ignoring the term “canonical” because I don’t know what it means in this context. It may imply an assumption that is inapplicable to the issue we’re attempting to address, namely, whether the atmosphere would “try” to impose a lapse rate even in the absence of essentially adiabatic convection.

If I understand it correctly, Velasco et al. show, by the fact that the velocity-and-altitude distribution of their Equation 5 is not the product of the altitude and velocity distributions of Equations 6 and 7, that the two variables are not statistically independent. (Note that Equation 7 gives the velocity distribution of the gas as a whole; it is silent about the distribution at any given height.)

However, this means rather less than it appears. In the limit, Equation 5 approaches Roman et al.’s Equation 43, which is indeed the product of a factor dependent only on altitude and one dependent only on height, as Coombes and Laue assumed. And, for numbers of molecules and energy levels relevant to the earth’s atmosphere, it appears to me that the result is negligibly different from the limit value.

Joe Born says:
January 11, 2012 at 3:24 pm“…Even though I’ve yet to find the answer, I have greatly appreciated the learning opportunity this forum has presented–and I haven’t finished mining it…

Hi Joe, until the heavy-weights turn up, here are the ideas of a someone who has more experience of experimentation than theory, for what it’s worth. One of the lessons I quickly learned was that often results didn’t give the exact match to what the theory predicted and most theorists I talked to about variation would always put it down to experimental error. However, often the theoretical model doesn’t match the real world for a variety of other reasons, so a divergence is perhaps to be expected when dealing with models of our complex and turbulent atmosphere.

Regarding the statistical mechanical models used for gases, there are several assumptions made to simplify understanding. An ideal gas is used, in which the individual molecules have no size, no attraction due to gravity/other force, and all impacts that occur are totally elastic. The models also assume other fields (charge, magnetic, cosmic ray, etc) are either non-existent or have no effect and often assume an equilibrium state.

Back in the real world our atmosphere is a much messier place, with turbulence and varying energy inputs of different types happening every nanosecond at different altitudes. These factor tend to be an enormous confounding factor to our understanding of what’s happening and the mechanisms involved. Finally, I find the match between Nikolov and Zeller’s calculations using lapse rates and actual temperatures observed for Earth and other planets very convincing, even without a good statistical model of how molecules behave.

I, too, think there may be something real in the results Nikolov & Zeller found (although the moon and Mercury drop from the curve when you graph N&Z on a log-log plot), but it’s far from clear that the results they found necessarily imply there’d be a lapse rate at equilibrium. Also, their description was, to be charitable, impressionistic–perhaps partly understandable, since it was just a poster. And . . . well, I’ll stop here; I’m in no position to criticize others’ clarity of exposition, as you can see from my phase-space discussion above.

In any event, I take your meaning about the divergence between theory and practice, although I’m struggling to find a way of applying it to the question before the house. My impression is that none of the writers believes that their equations describe reality; they’re merely addressing the question of whether a significant lapse rate would prevail if there were no turbulence, there were no convection, the molecules were all monatomic, the lark were on the wing, etc. I understand Velasco et al. and Coombes et al. to say the lapse rate would be either nonexistent or negligible, while I understand folks like Hans Jelbring believe it would be significant–if their theories about the relative irrelevance of greenhouse gases is correct.

So this may be a case in which theory is important even if it diverges from the real world.

Joe Born says:
January 11, 2012 at 6:58 pm“…So this may be a case in which theory is important even if it diverges from the real world…”

Yes, Joe, I too believe that it is ultimately vital for progress that we fully understand, not just this, but other fundamental things like ‘what is gravity?’, for example.

At the moment, however, when we, the citizens of the west are being asked to pay large sums of money to rescue the world from CAGW with it’s mythical link to CO2. I think that providing the methodology used by Jelbring and Nikolov-Zeller works, as it appears to do regarding other planets and Earth, it is more important to use this information, even without a full understanding, to help us understand climate – just as we use the very useful empirical gravity formulae of Newton and Einstein understand orbits.

In the medium term I would like to see more and bigger scale experiments being done which better simulate real world conditions to get better observations to help the theoretical work. Until we do I’m afraid we’ll waste time tilting at windmills.

Velasco et al were using what’s called the “Micro-Canonical Ensemble”.

A short summation of the Ensembles:
Micro-Canonical Ensemble: N, V and E are constant.
Canonical Ensemble: N and V are constant. T is constant at a specific point (reservoir contact).
Grand Canonical Ensemble: V is constant. T is constant at a specific point.

Regarding the Velasco et al “infinite case”, that only makes sense if the gas is either infinitely large or not quantized (ie non-atomic). I actually agree with that bit of analysis. If the gas is continuous rather than atomic, the temperature difference goes away. It is the quantization (finite case) that breaks the detailed symmetry.

Could you explain a little more what you mean by “continuous rather than atomic”? I assume you’re simply agreeing with my assessment of Velasco et al.’s applicability: if the number of particles and total energy gets large enough (“approaches infinity”), the lapse rate is negligible at the altitudes we encounter on earth–and those quantities are large enough in our atmosphere. I assume you don’t mean that the results have no real-world implications because the derivation is classical: although it assumes a finite number of molecules, the number of microstates is taken to be uncountably infinite rather than, as quantum mechanics would have it, finite (but large). If I understand their paper, Velasco et al. assume an atomic gas at all times, although the number of molecules approaches infinity for some of their equations.

I am sorry, but I have lost the plot here. I have not had the time to read all of the papers, but this thread does interest me – primarily from a thermodynamic standpoint.

I do not understand: ” if the number of particles and total energy gets large enough (“approaches infinity”), the lapse rate is negligible at the altitudes we encounter on earth–and those quantities are large enough in our atmosphere”. In my simplistc view there are two lapse rates, pressure and temperature – the first is caused by gravity and the mass of the atmosphere and the second is a consequence of the gas laws (PV = nRT). I realise matters are much more complicated than this, but what am I missing? Is it that if n were infinite, the whole universe would be filled with air?

First, remember that I’m not saying I know this stuff; I’m just saying the way it sounds to a layman, in the hopes that someone authoritative can set us all straight.

But, the way I read Roman et al.–which was written by the same guys who thereafter wrote the Velasco et al. critique of Coombes & Laue–pressure in a thermally isolated vertical column of a monatomic ideal gas at equilibrium would indeed fall with altitude, and at a rate similar to what we observe in the earth’s atmosphere, but the temperature drop with altitude would be negligible for large numbers of molecules and amounts of total energy. Velasco et al.’s Equation 8 gives the temperature distribution. When I plug numbers in, I get no significant temperature variation.

E is the total column energy for all the molecules: take every molecule, add its kinetic and potential area, and repeat for all molecules. So, although an individual molecule’s potential energy is dependent on its height, the aggregate energy E has no particular height.

The last expression in my function VRW_Eqn8() is from Velasco’s Equation-8 expression for kinetic energy as a function of height. The final expression is the R code divides the kinetic energy by Boltzmann’s constant

Joe Born says:
January 12, 2012 at 10:53 am‘…pressure in a “thermally isolated” “vertical column” of a “monatomic ideal gas” “at equilibrium” would indeed fall with altitude, and “at a rate similar to what we observe in the earth’s atmosphere”, but the “temperature drop with altitude would be negligible for large numbers of molecules and amounts of total energy”. Velasco et al.’s Equation 8 gives the temperature distribution. When I plug numbers in, I get “no significant temperature variation”…’

Hi Joe, thanks for the above post which clarifies some of the assumptions made. I think there are several disconnects/simplifications between the physics used in the ‘thought model’ and what happens in reality, as follows:-

“thermally isolated” – Never happens in the real world of constant energy change.

“vertical column” – Due to side winds, Coriolis effect, tidal effects from moon – not reality. Also the nature of the gas column changes as the lower atmosphere is well shielded from energetic radiation like UV, gamma rays, cosmic rays, which cause ionisation and complex chemical changes.

“monatomic ideal gas” Only the inert noble gases are monatomic. Real world gases are mainly diatomic molecules with a γ-factor (Cp/Cv) of 7/5 for ‘ideal’ model which includes rotational energy, as opposed to 5/3 for ‘ideal’ diatomic gases where rotational energy is zero (spin in both instances is a different matter). Real world atmospheric gases are also chemically reactive and effects from this is ignored by model.

“at a rate similar to what we observe in the earth’s atmosphere” – due to factors mentioned above, it looks like the effect of gravity is significant and well represented by model.

“temperature drop with altitude would be negligible for large numbers of molecules and amounts of total energy” – If your maths are correct, the model fails. In the real world, the temperature drop with altitude is observed in the troposphere, then changes at higher levels…

This change seems to be due to reduced gravity an increase in turbulence and a dramatic increase in ionising radiation.

“no significant temperature variation” – the model fails to model observation of how real gases behave in the real world, because of wrong assumptions made in the base equations.

To make progress on understanding climate we need to do more experimentation and have more detailed, accurate observations. I think we also need to develop better tools to understand the effects of both MEP and the spatio-temporal chaos evident in our complex, dynamic, interlinked weather/climate system.

We are entirely in agreement that the model and the real world diverge. But that’s rather the point; if Roman et al. (and my understanding of what they’re saying) are right, then our atmosphere’s substantial temperature lapse rate, which no one has denied, or, if they have, I missed it, is likely caused by the atmosphere’s constantly being driven from equilibrium rather than, as many who are more qualified than I contend, by its seeking equilibrium. So there would seem to be some value in resolving the question of an isolated ideal gas’s equilibrium behavior, differences between the real and the ideal notwithstanding.

Again, I think we agree, although I confess to not quite comprehending your point about the prevalence of diatomic gases in the atmosphere. I would have thought that, if the equilibrium lapse rate is negligible for a monatonic gas, it is negligible a fortiori for a diatomic gas. No doubt you perceive a subtlety that has eluded me.

For that matter, there is every reason to believe that Roman et al. and/or my interpretation of their work is wrong in general; I’m just hoping someone will explain what their/my error is.

Since N and E are fixed in the micro-canonical ensemble, we can choose any point on the phase-space surface, and evaluate it regardless of probability. The point I choose to evaluate is all molecules at height z=E/mg. The term (1-mgz/E) is 0, which says that there is no thermal energy left. This fits with conservation of energy, with all thermal energy converted into potential energy. Working backwards, the z term must mean the average z, as any other meaning would violate conservation of energy.

That produces a much more substantial lapse rate. Unfortunately, the equation appears to be difficult to use to extract an actual temperature profile, as it’s not in that form.

As for the infinite case, I actually meant the decidedly non-physical meaning, a non-atomic gas. If a gas isn’t atomic (at any level, but rather a continuous effect), the temperature profile will be uniform across an undisturbed column, even in a gravity well. The statement is useful only for describing how actual gases diverge from the infinite case.

Tenuc,

The micro-canonical ensemble is a simplified model, really only useful for qualitative analysis. Your objections are all valid.

Q. Daniels, thanks for that. I’d been wondering. For tthe last few days I’ve been calling into one of the libraries on campus to peek at a 1970 thesis which examines Maxwell’s sources and influences. he developed many of his ideas on the statistical mechanics of gases from interactions he had with Clausius. Also, he published his main paper on the mechanics of gases not long after developing a statistical method for dealing with the collision interactions of the masses composing Saturn’s rings.

I’ll reiterate something I asked quite early in the N&z thread.

“Are we still working with the thought experiments Maxwell did a century and a half ago regarding the kinetics of gases?”

Has there been a development of empirical analysis and theoretical curves for the behaviours of mixed gases like air at various temperatures and pressures? It’s a subject I know little about. More of a metals and hydraulics man myself.

Could you break down your reasoning into bite-size steps that someone a little less nimble can understand? I’m afraid the discussions on these subjects usually reach their destinations before I’ve pulled my mental boots on.

I was with you up through “Since N and E are fixed in the micro-canonical ensemble, we can choose any point on the phase-space surface.” Or at least I think I was with you; I interpreted “surface” to mean the the set of points (which I picture forming a hyperparaboloid) in phase space where the state density is non-zero.

But then you say, “The point I choose to evaluate is all molecules at height z=E/mg.” According to my reading of Roman et al.’s Equation 2, from which Velasco et al.’s Equation 8 was ultimately derived, the state density at that point (or, since there can be different x and y coordinate for the same z value, those points) is zero; the potential energy of each molecule can’t equal the total energy of all molecules unless N = 1, a case for which I agree that Velasco et al. would arrive at a significant lapse rate.

Indeed, the only way putting even just a single molecule at E / mg can place the system on that nonzero-state-density surface is to have all the other molecules stationary at z = 0.

But let’s ignore those difficulties and consider a system in which the average molecular energy is only 200 Kelvins times the Boltzmann constant and the system consists of only a single mole in an arbitrarily high one-meter-square column. Blindly plugging the numbers into z = E / mg for that system will by my reckoning yield an altitude on the order of 3.5 x 10^27 meters, where the assumption, on which Equation 8 is based, of constant gravitational acceleration g has long since lost validity. In fact, without doing the math, my guess is that a single molecule’s potential energy in that system could not reach E even at an infinite altitude.

But I digress. Here are my questions. How do you get from the difficulties your hypothetical poses to z’s being mean altitude? And where in the equations do you see the authors dropping the assumption of an atomic gas? I see N throughout their equations; at worst N becomes countably infinite.

Joe Born, you’re right to spot a mistake in my work. I suspect myself of sloppiness right now, and respect your stubborn care. It’s always worth double-checking my work. Your meaning of “surface” is as I intended.

Evaluating z=E/mg allocates all the energy to one molecule. z=E/m*g*N would be the height were all molecules were at height z with KE 0.

As for the infinite case, that’s in equations 9 and 10. If you assume a finite volume, the only way to get an infinite number of particles is if they’re infinitesimal, or effectively non-atomic. For any atomic size, they remain a finite number.

Just for the benefit of readers who may miss the implications, it remains true that, at least to the extent that we understand them, Roman et al. and Velasco et al. say there’s a temperature lapse rate at equilibrium for an isolated ideal-gas column in a gravitational field but that, for bottom-level pressures on the order of that we encounter at sea level, the temperature lapse rate is negligible.

That’s interesting Joe. Over on the solar thread Tim C commented that there doesn’t seem to be much of an effect in deep caves etc. Can you think of any reason the effect might tail off once the pressure goes over 1 bar? Conversely, I wonder if the effect is comparatively much stronger at higher altitudes. Tricky one to test that’s for sure.

I suppose conceptually, there might be a logarithmic falloff due to factors such as free path lengths rapidly diminishing once density reaches a certain point. Not that I could quantify it from my little knowledge of the molecular kinetics involved.

I put some effort into unearthing useful material from underground. Nothing suitable appeared although a lot of interesting stuff is around. There do seem to be unknowns, unexplained excesses yet nothing clear anywhere.
A further point to add to the experiment, it ought to be carried out in a pressure sealed outer chamber.

An example document
MICROMETEOROLOGICAL MODELING OF AN
IDEALIZED CAVE AND APPLICATION TO
CARLSBAD CAVERN, NM

I get a much steeper lapse rate than you do. For T=288 K, m=0.029 kg/mol, I get z=8.4 km. That doesn’t translate directly into a lapse rate, because N drops with altitude in any probable configuration. That just says that the kinetic energy of air at 288 K is enough to lift it to 8.4 km.

Tallbloke asked, “Are we still working with the thought experiments Maxwell did a century and a half ago regarding the kinetics of gases?”

“The science is settled.” That does not, however, mean that it is correct.

If what you mean by “there doesn’t seem to be much of an effect in deep caves etc.” is that air temperature does not in general continue rising with decreasing altitude when you’re talking about caves, I know nothing more than the guy on the next bar stool, who might guess that cave temperatures are dictated by those of the enclosing soil or rock, which acts as a low-pass filter of surface temperature so that cave temperature tends to be the annual average of the temperature at the surface.

I have read the two papers now that say such a column would be isothermal all of the way to the top and it caused me to consider what implications would appear if that was in fact true. I did think that same way a year or so back, when talking of what the temperature would be if the atmosphere contained no greenhouse gases, I know, that has been beat to death. But if there is no real natural lapse tendency then a pure nitrogen or argon atmosphere would make this one hot planet. There would also be no water at the surface in that case.

The sun, all of its power, no clouds, would radiate the tropic band in a range of about 1100-1368 W/m2, that accounting for a large percentage of earth’s area on the lit side, and would raise the temperature of the surface very high and by conduction and convection only would heat the air in bulk, but no radiative cooling occurring. At night all convection would cease and even though the soil would get very cold the atmosphere could only cool by slow conduction, no convection present, and always in an inversion on the dark side. Eventually the entire atmosphere all of the to the top would be quite hot, I have read one calculation placing it at about 60+ degC average.

So in that case, if those papers are correct, we do need greenhouse gases not to warm but to cool our atmosphere. Hmm… that sure would flip the agw proponents, the ipcc and the general consensus’s logic completely upside down.

See, I always thought the solar radiation on the GHG’s and ozone were *warming* the stratosphere and that is why the lapse rate turned vertical above the tropopause, but if the lapse is naturally straight up we might have to rethink exactly what it is that alters these turns in the lapse. Have we been looking at this wrong for so many years?

Any atmosphere, whether composed of GHGs or not reduces the ability of the surface to radiate to space by diverting some of the surface energy to conduction into the atmosphere which warms up to match the surface temperature.

Applying the Ideal Gas Law then redistributes the energy in the atmosphere to create a temperature gradient from surface to space.

Due to the atmosphere having the highest temperature just above the surface the effect of the Ideal Gas Law feeds back to the surface by reducing the rate at which the surface can conduct and radiate energy upward with the result that the surface can then itself achieve a higher temperature in reponse to the same level of solar energy input.

Thus the equilibrium temperature at the surface rises as a result of atmospheric density and pressure.

That is the Greenhouse Effect.

The radiative abilities of the atmospheric gases are relevant to the patterns of energy movement between surface and space but do not affect the surface temperature unless they also significantlly increase atmospheric mass

I’m not certain that I follow the trail of logic between a molecule’s potential energy at 8.4 km equaling its kinetic energy at 288 K and the conclusion that the lapse rate is significant. Could you drop some bread crumbs for me?

Again, the way I got the lapse rate was to do it numerically by executing the R code I included in one of the responses above. But we could also do it analytically: differentiate Velasco et al.’s Equation 8 with respect to z and divide by k: lapse rate = -[f/(fN + 2N -2)]mg/k.

I believe that N is a value that applies to the set of molecules as a whole, so “N drops with altitude” may not be correct.

Q.Daniels, yes, that’s why I had a hunt for theses rather than fat tomes written by people long inculcated in the mainstream paradigm.

Joe: Good point about cave walls. What about the temperatures at Jericho Tim C drew our attention to a couple of weeks ago? They seems to indicate an effect.

Wayne: Thought provoking stuff. There are those who say co2 acts primarily as a cooling agent. I’d thought that might be too controversial to get into, but it may be important. The next scare: “We gotta cut co2 ‘cos it’s cooling the planet fast!” :):(

Stephen: You said:
“Applying the Ideal Gas Law then redistributes the energy in the atmosphere to create a temperature gradient from surface to space.

Due to the atmosphere having the highest temperature just above the surface the effect of the Ideal Gas Law feeds back to the surface by reducing the rate at which the surface can conduct and radiate energy upward with the result that the surface can then itself achieve a higher temperature in reponse to the same level of solar energy input.

Thus the equilibrium temperature at the surface rises as a result of atmospheric density and pressure.

That is the Greenhouse Effect.”

Yes, that’s pretty much the formulation I came up with on the N&Z thread yesterday (actually I wrote it in an offline email to Willis Eschenbach in response to his objection to Jelbring’s theory).

I was a bit disappointed no-one responded. I said:

I’m going to ‘put it out there’ and give a very brief synopsis of what I currently think the Jelbring and Nikolov-Zeller hypotheses are saying. Hopefully, the feedback will help me develop my understanding further.

If the adiabatic lapse rate observed in an ideal gas atmosphere is set up by gravity as Jelbring, N&Z, Loschmidt, Gilbert, Brooks (and maybe the people who came up with g/Cp?) claim, then the high altitude air at the top of a transparent atmosphere is going to be at a cooler temperature, and the near surface air is going to be at a higher temperature than that which it would be at if that atmosphere was in isothermal balance. Energy is conserved and equally distributed overall, as it must be according to the first and second laws of thermodynamics.

That is going to warm the surface (by conduction) to a higher temperature than the Sun would warm it to in an isothermal atmosphere and that is going to cause the surface to radiate at a temperature higher than that calculated by the S-B equation.

I think that between the two of us we have pretty much nailed ‘the elevator speech’ here. Perhaps we should work together on honing it to sharpened perfection, and then drive it through the heart of the co2 Witch.

Stephen’s formulation has jogged another thought in my battered brain. The rise in temperature of the near surface air will feed back to the surface, this will feed back to even higher temperature near surface air. This positive feedback (eventaully limited by evaporation and covection) will mean the surface temperature has a heightened sensitivity to small solar variations…

It follows that IR sensors pointed at the sky are not measuring downwelling IR from GHG molecules higher up.

All they are measuring is the warmth of the air molecules directly in front of the sensor and those warmer molecules (whether GHGs or not) have been warmed by operation of the Ideal Gas Law (which automatically causes warmer molecules to be found lower down in the atmosphere) and NOT by so called downwelling IR.

There is no need to propose any downwelling IR at all. The warmth is already present in the lower molecules by virtue of the Ideal Gas Law working via pressure and density.

“I think that between the two of us we have pretty much nailed ‘the elevator speech’ here. Perhaps we should work together on honing it to sharpened perfection, and then drive it through the heart of the co2 Witch.”

Thank you all for a very interesting discussion, I have learned a lot (mostly about how much I don’t know!).

Joe, I think that you have answered my question of yesterday in your answers to others. Thanks.

Tallbloke – I very much applaud your effort to summarise the situation in a single paragraph. As a first effort it looks good to me, and with some tidying up could become very useful (Tallbloke’s Conjecture?).

I tried to do a similar thing from the standpoint of entropy over on BH, and like you was dissapointed that it only drew one response (you can be certain that any attempt to summarise climate in a single paragraph is wrong – or words to that effect). However, I will try it here:

“Considering the entropy of the planet as a whole, including the conductive effects of the surface – gas boundary and with calculations performed within a boundary high above the top of the atmosphere, the lapse rate acts to maximise the entropy of a near – equilibrium thermodynamic system that constantly seeks equilibrium as a consequence of rotation. The laws of thermodynamics subsume the effects of all energy transport mechanisms – conduction, convection and radiation.”

I also included a provocative statement:

“The implication is that only insolation, gravity, rotation and the mass of the atmosphere are responsible for “climate”. Doubling, tripling or whatever the mass of CO2 will have a negligible effect on the total mass of the atmosphere, and hence would not lead to any measurable effects on the “climate”.”

I am by no means certain that the above is correct, so any criticism would be welcome.

“But if the surface is warmer per that alleged effect and the atmosphere is transparent, then you are radiating more to space than you are absorbing.”

I seem to recall having answered him to the effect that no atmosphere is transparent to conduction.

The critical issue is that conduction is slower than radiation so any increase in conduction relative to radiation will result in a higher surface temperature because the rate of energy flow through the system is being reduced and energy is building up within the system as a consequence.

ANY atmosphere will do because only mass matters. The more mass, the more conduction relative to radiation, the slower the rate of flow and the higher the temperature at equilibrium.

I can’t follow your elevator speech, so maybe there will be others, too, who will struggle to understand it.

Here’s your formulation:

“If the adiabatic lapse rate observed in an ideal gas atmosphere is set up by gravity as Jelbring, N&Z, Loschmidt, Gilbert, Brooks (and maybe the people who came up with g/Cp?) claim, then the high altitude air at the top of a transparent atmosphere is going to be at a cooler temperature, and the near surface air is going to be at a higher temperature than that which it would be at if that atmosphere was in isothermal balance. Energy is conserved and equally distributed overall, as it must be according to the first and second laws of thermodynamics.

That is going to warm the surface (by conduction) to a higher temperature than the Sun would warm it to in an isothermal atmosphere and that is going to cause the surface to radiate at a temperature higher than that calculated by the S-B equation.”

Does “cause the surface to radiate at a temperature higher than that calculated by the S-B equation” mean that the area integral of the product of emissivity, the S-B constant, and the fourth power of surface temperature exceeds total insolation?

If so, let’s join the action at a point in time at which the situation you describe prevails: the warm lower atmosphere has warmed the surface to a temperature at which it is radiating out more power than it is receiving from the sun. This tends to cool the surface, but the lower atmosphere tends to counteract that cooling. For the lower atmosphere to warm the surface, though, the lower atmosphere has to be cooled by the surface, so its temperature falls.

But, you may say, gravity then compresses the atmosphere further, doing work on it to restore the lower-atmosphere temperature. Given that the atmosphere is perfectly transparent, though, the only sources of atmospheric energy are the surface and gravity, so gravity’s attempting to maintain surface temperature–against the fact that the surface radiates away more power than it receives–ultimately compresses the atmosphere to nothing, an effect no one has yet observed.

I assume I’ve misrepresented your elevator speech’s meaning, but I don’t see where, so you may want to add or remove something to prevent hearers from arriving at the conclusion I did.

“For the lower atmosphere to warm the surface, though, the lower atmosphere has to be cooled by the surface”

Joe: I don’t follow this bit (among others). :)

It seems to me there will be a positive feedback until it is balanced at a higher T by convection.

the net effect of the gravitationally induced temperature gradient will then be to raise the surface T to a temperature above that calculated purely from the Stefan-Boltzmann eq. Given that no atmosphere is in reality transparent, the increased (by T^4) radiation to space from higher up will rebalance the energy budget.

I’m not sure what led to your interpretation yet, but I’ll work on it, because clear communication of ideas is what I strive for. Thanks for the input.

I think you may have put your finger on the source of the confusion: “Given that no atmosphere is in reality transparent.” What I–and perhaps Willis–had understood you to say was that it would make no difference if no radiation at all were absorbed by, or originated from, the atmosphere. If that assumption is dropped, then your formulation seems plausible (to me, for the moment). What you may be saying is that beyond some minimum but necessary level of optical density other weather processes conspire largely to neutralize any effect that further greenhouse-gas-concentration increases would have on average surface temperature. I might add that such a possibility had suggested itself to me as I observed the back and forth over the issue.

Just in case it remains relevant, what I meant by “For the lower atmosphere to warm the surface, though, the lower atmosphere has to be cooled by the surface” is that the atmosphere must lose heat to the surface if the surface is to absorb heat from the atmosphere. Perhaps “cooled” was inappropriate because, as I understood your hypothetical, work performed on the atmosphere by gravity in further compressing it would make up for the heat the atmosphere transferred to the surface and would thereby keep the temperature at the bottom of the atmosphere from dropping; i.e., the bottom of the atmosphere would not be “cooled.” This may all be irrelevant, though, since it was an attempt to investigate a hypothetical situation I now recognize as different from the one you’ve posed.

Incidentally, consideration of your formulation may in a sense be largely orthogonal to the question of whether an isolated vertical column of an ideal gas would exhibit a temperature lapse rate at equilibrium; you’re (rightly) requiring processes such as convection that impose decidedly non-equilibrium conditions, so the insensitivity to further greenhouse-gas increases for which you argue may prevail even if the lapse rate we observe would not prevail at equilibrium.

OK, we’re mostly on the same page now. My original formulation was in response to Wilis’ concerns about the Jelbring hypothesis, which does have a transparent atmosphere. However, the model specified also prevents any radiation to space so Willis’ argument doesn’t apply.

Your further obs are interesting, and how much it matters whether the column has a gravity induced lapse rate or not depends on the question of what ‘back radiation’ gets up to in a schema where there is no gravity effect.

Rog, this is what you said to Willis as referred to in your post above:

“If the adiabatic lapse rate observed in an ideal gas atmosphere is set up by gravity as Jelbring, N&Z, Loschmidt, Gilbert, Brooks (and maybe the people who came up with g/Cp?) claim, then the high altitude air at the top of a transparent atmosphere is going to be at a cooler temperature, and the near surface air is going to be at a higher temperature than that which it would be at if that atmosphere was in isothermal balance. Energy is conserved and equally distributed overall, as it must be according to the first and second laws of thermodynamics.

That is going to warm the surface (by conduction) to a higher temperature than the Sun would warm it to in an isothermal atmosphere and that is going to cause the surface to radiate at a temperature higher than that calculated by the S-B equation.”

Could it have been prompted by this email that I sent to you previously ?:

“Does this make sense ? :

“The heat within a campfire would get hotter with more molecules (increased air
density) around the flames because the heat energy is moved away more slowly
due to the higher number of molecular collisions.. So the density of the air
around the campfire increases the temperature gradient from fire to
observer. In effect the denser atmosphere obstructs radiation leaving
conduction relatively more important. Conduction is a slower process than
radiation so the temperature within the flames rises

In exactly the same way the denser the Earth’s atmosphere the hotter the
surface becomes and the steeper the temperature gradient upward because
space remains at the same temperature but the surface gets hotter. Just as
with the campfire the solar energy hitting Earth’s the surface is moved away
more slowly because the role of slow conduction is enhanced relative to that
of fast radiation as a result of the greater atmospheric density.

Density of the air at the surface is a result of the strength of the
gravitational pull of the entire planetary mass and the mass (not
composition) of the atmosphere.

So, indirectly, through pressure and then density, gravity does determine
the lapse rate and it is mass dependent and not composition dependent so
Oxygen and Nitrogen are involved despite being relatively non radiative.
Oxygen and Nitrogen participate fully in adding to the process of conduction
in its competition with radiation.

The ability of increased conduction to slow down radiative energy loss is
what relegates radiative processes to a secondary role and explains why it
is gravity rather than radiation that sets the lapse rate.

Gravity and density alter the balance between fast radiation and slow
conduction. If one reduces radiation and increases conduction the heat
content and temperature will rise given the same energy input.”

I think it sidesteps a lot of the problems if one regards density as
shifting the balance from fast radiation to slower conduction giving a rise
in equilibrium temperature as a consequence.

After all, no atmosphere means an immediate turnaround of energy i.e.
radiation straight in and straight out pretty much instantly. As soon as one
adds an atmosphere capable of CONDUCTION which includes non GHGs then the
conduction takes away from the efficiency of the radiation process by
slowing energy dissipation down which is what then leads to the higher
equilibrium temperature. The denser the atmosphere the more conduction takes
place before the radiative energy can be released to space and the higher
the equilibrium temperature rises.

So, radiative processes are not in control because they are subject to
interference from density and the consequent increase in conduction.

Convection and the water cycle then act to try to reduce the slowing effect
on energy dissipation of more conduction but can never get back to the
efficiency of raw, in/out, radiation.

” how much it matters whether the column has a gravity induced lapse rate or not depends on the question of what ‘back radiation’ gets up to in a schema where there is no gravity effect.
This seems to be the battleground for the ‘sides’ in the debate.”

If there were no gravity effect the energy conducted to the atmosphere from the surface would be far more evenly distributed through the atmospheric column.

The surface temperature would be closer to the black/grey body calculation.

GHGs would still radiate both up and down and might well find it easier acquiring energy by collisions from warmer non GHG molecules around them at higher levels.

Their cooling capability from their ability to radiate upward might be enhanced in the absence of a gravitational effect.

Given that virtually all energy in the air would still be from upward conduction from the surface I don’t see that GHGs would have any significant contribution other than via enhanced cooling.

As it is, the so called ‘back radiation’ might just be the temperature of the lower level molecules right in front of the sensor and may not represent upper atmospheric ‘heat’ at all.

stephen: ANY atmosphere will do because only mass matters. The more mass, the more conduction relative to radiation, …

I now see your point. If the air at the surface is very thin and diffuse, little conduction will occur, mostly radiative loss. But if the air is heavy and dense from more mass, the radiation will remain the same but conduction will be much higher, and, with that, convection will be much higher keeping the low atmosphere much warmer, GHGs or not.

I still say that generally radiation is but fast conduction in an absorbing atmosphere (plus it’s ability to escape to space if never absorbed). More mass would shift the radiative/conduction ratio toward the slower conduction side as you were saying.

Roger, a further note. To me that does not yet affect my view on N&Z’s paper. I still think the gradient tendency on all planets is there and real. But as usual, I’m just searching for the specific mechanism, you know, the relations between all of these factors that makes it jell and makes perfect physical sense in observations. I have some thoughts on that but will go into the details later. Didn’t want you to think the DALR by itself made any difference but Born and Eschenbach may be right on that front.

Stephen, that’s a great point. In the back of my mind I was always questioning why Graeff went with water instead of air. I have already toyed with that, like g/(Cp*rho) extending the DALR of g/Cp but that will take a while to check out, but, thought tallbloke might needed that thought up front.

In the unlikely event that anyone has used the R code I provided above for evaluating Velasco et al.’s Equation 8, I should mention that the last line results in a value that is 50% too high. It should read “(2 / 3) * VRW_Eqn8(z, f, E) / k”

Afaik the ALR doesn’t work in fluids because they are not compressable.

Observations seem to prove the accuracy of the DALR.
When surface air temperature and dewpoint for a given location are known, you can calculate at which altitude a parcel of air will start to condensate (changing to the WALR) when it rises, as thermals do. These cloudbase forecasts are ususally very accurate.

If this all about whether gravity causes a temperature gradient in an atmospheric column then…

If the column is heated from the bottom and cooled from the top like is on the earth then yes, Virginia, there will be a temperature gradient due to gravity and that gradient will be there even if the atmosphere is pure nitrogen.

The key to understanding this is knowing that air is conductively heated and radiatively cooled. At the surface where the conductive heating occurs density is higher and more collisions between molecules occur. These collisions keep the energy entrained in the air mass with the molecules basically just passing it back and forth between them. Of course they must also radiate as all matter above absolute zero radiates. Because it’s all nitrogen when a photon is emitted it won’t be absorbed and it either leaves the system at the speed of light or is reabsorbed by the surface if emitted downward.

As one progresses upward in the atmosphere and density falls there are fewer collisions and more photon emissions. Thus a temperature gradient from surface to space is established.

I guess the big question is whether this establishes a greenhouse effect even though there are no greenhouse gases in our hypothetical all-nitrogen atmosphere.

The answer is no. Conductive heating ceases once the nitrogen in contact with the surface reaches the same temperature as the surface. At that point it’s entirely radiative and the thermal IR from the surface passes straight though the nitrogen like it was vacuum. Thus all you’ll get from this is an S-B temperature at the surface and a lapse rate from there up to TOA.

“Except that the incoming solar energy to the surface continues at the same rate whilst the removal of energy to the air is slowed down. Thus does the surface reach a higher equilibrium temperature than that predicted by S-B.”

No Stephen. Equilibrium is established at S-B temperature and it’s then like the gas isn’t there at all. All that happens is the gas at the surface reaches the S-B temperature and temperature gradient between that and TOA is established. For S-B temperature to be exceeded requires a fluid that can absorb thermal radiation. A totally transparent medium doesn’t fit the bill. It simply heats conductively to whatever temperature the surface is at (reaches equilibrium) then drops out of the picture.

If the Ideal Gas Law and the lapse rate that results from it places the warmest molecules of air at the surface then conductive exchanges with the surface would elevate the equilibrium surface temperature wouldn’t they ?

Those warm molecules at the surface will be warmer than the average temperature of the atmospheric column by virtue of the lapse rate. The lapse rate itself causes a feedback to the surface via downward conduction from the warmest molecules in the atmosphere.

The atmosphere is a fluid that can absorb thermal energy via conduction. It doesn’t have to do it via radiation.

Reality does not present us with a totally transparent gas, it does not exist. IR does not leave at the same frequency that it arrived. Solar energy does not leave at the same speed as it arrives, only the amount that leaves has to balance the amount that arrives. The slower speed of leaving results in the real greenhouse effect. pg

BenAW: “Observations seem to prove the accuracy of the DALR.
When surface air temperature and dewpoint for a given location are known, you can calculate at which altitude a parcel of air will start to condensate (changing to the WALR) when it rises, as thermals do. These cloudbase forecasts are ususally very accurate.”

Hey thank Ben. I think you might have misunderstood me. The DALR seems to stand out there by itself. It is accurate I know. Studying some skew-T and radiosonde graphs, for some reason I never come across anything in the pressure or temperature that show that physical ‘matter’ in pressure or temperature respect the DALR line.

Do see where I’m pointing? If it is really a physical limit or an equilibrium line, or, what temperatures respect and line up to in reality you should see at some point some evidence of it on such graphs. Otherwise it is just an indicator or ratio. Like the market, the price lines on a graph are real, they are prices of real assets, all of the indicators at the bottom are just mathematical tools that are supposed to (I wish) show you some aspect in relation to the prices but the indicators themselves are not real, they are of a mathematical nature. If you can help I would appreciate it. In that light is the DALR and indicator of properties in an atmosphere or is it real.

I’ve read so much on the various lapse rates but still don’t have that answer.

BenAW, come to think about it, is that the line a radiospnde would find if there was zero water vapor in the air. That would explain why I never see anything follow it. I just went, duh, I should have homed in on that thought a few days ago! Do you ever sometimes fell rather dense, miss something that is right under your nose but you are too tangled in the details? ☺

In my meteo education the DALR and WALR have been explained as the temp. change a parcel of air experiences when it RISES (or descends), WITHOUT exchanging energy with the surrounding atmosphere.
The temp. a radiosonde measures when it ascends is just that, a recording of the actual atmospheric temp. By coincidence this temp. may have over some range the same value as eg. the DALR.
I feel talking about the atmospheric temp. profile as adiabatic is confusing.

BenAW: The reason that temperature of that air parcel changes by that amount due to its decompression/compression is exactly because the DALR matches the pressure change of the atmosphere due to gravity. That’s the whole point.

That’s understood. My point is that you can’t talk about the temperature profile (environmental lapse rate) as being adiabatic. The temp. profile can be stable, indifferent or instable. Indifferent is when the profile happens to match the DALR.

Sorry, folks, the web site ate part of the equation in my last post; it must not have liked the mean-indicating angle brackets

Here it is without the mean-indicating brackets:
K = (3E/(5N-2))(1-mgz/E),
where K is mean single-molecule kinetic energy, N is the number of molecules, E is total system energy, m is molecular mass, g is the acceleration of gravity, and z is altitude.

As I said before: Place the two monatomic molecules by themselves into the isolated thought-experiment column we’ve belabored. Have them share a total (potential + kinetic) energy of 2mgz_mid. Let them equilibrate. When we plug this little system’s values into the equation above, which is adapted from Velasco et al.’s paper, we get (3/4) mgz_mid(1 – z/z_mid) for the mean per-molecule kinetic energy in our gas column.

According to Velasco et al., that is, the mean per-molecule kinetic energy in our gas column is 0 at 2z_mid, (3/8) mgz_mid at z_mid, and (3/4) mgz_mid at the bottom of the column. On the other hand, Brown, Eschenbach, and the many physicists whom I hereby thank for having patiently given their time here to “fight the amazing ignorance of thermodynamics [that I’ve] so ably demonstrated” say that the mean kinetic energy at equilibrium is independent of altitude: it’s the same at z=z_mid as at z=0.

[…] of the apparent contradiction of the second law of thermodynamics, detailed in the well commented Loschmidt thread here at the Talkshop in January. Strong contributions were made by physicists and mathematicians, […]

[…] the engineering concern owner who has been experimenting with equipment he has designed to test the Loschmidt gravito-thermal effect. This line of research is highly relevant to the theoretical work of Hans Jelbring, and also […]

[…] the time of Maxwell, if it was good science?? Actually there was one good scientist, Loschmidt, who did dispute Maxwell. The really extraordinary thing is that until Graeff, nobody had checked Loschmidt’s […]

If gravity induces a temperature gardient in a gas why not a liquid? There is a negative lapse rate in the ocean caused by surface warming but without it it would be isothermal.

So if we built a large hollow cylinder and filled it with water, surrounded it by gas in a gravitational field, what would happen if the system was thermally isolated?

If everything ended up to be isothermal there would be no problem. But if there is a lapse rate in the gas, but not in the water, the resultant temperature difference between the air and the liquid would mean there is the possibility of constructing a Perpetual Motion machine of the second kind.

So, on this basis I’d have to go for isothermal. Does anyone disagree?

Are you assuming thermal isolation, but with perfect conduction between the water and the gas?

The water is incompressible, so would vary in pressure, but not density wrt height. The gas would try to form a lapse rate, and therefore heat the bottom of the water column. Convection would apply to both. The system would then seek equilibrium.

TT: It is, but it is overcome by opposite gradients caused by other factors. The Sun heating it from the top, and the convection assisted by internal tides and agitations. Maxwell talks about closed systems with all external forces excluded.

TB – my guess related to the impossible premise of “perfect conduction”, which is just as impossible as perpetual motion. There’s the rub – practical thermodynamics always gives a system increase in entropy.

There’s no assumption of perfect conduction between the air and the water in the column. Even if we apply an thermally insulating jacket to the cylinder, any local difference in temperature can still be exploited to the same effect. That can’t happen thermodynamically, so everything only makes sense if the equilibrium state tends towards an isothermal situation as Maxwell and Boltzmann argued.

I’d be interested to know what the temperature profile of the Arctic ocean was under a thermally insulating polar ice cap. I haven’t found any data on that yet but my expectation would be that it should be close to isothermal.

A couple of years ago when I first started to think about this, I thought that this was likely to be the case too. I did write, at the time, that if anyone wanted to observe the GH effect in action all they needed to do was climb a mountain and measure the temperature. I was later persuaded by some climate scientists, of mainstream opinion, that I was wrong and did withdraw that claim. But now I’ve swung back again to agreeing with Roy Spencer so I’m making it again!

I’m just wondering if mainstream science does have it right. For instance the University Of California are saying there still would be a lapse rate even without a GH effect.

A couple of years ago I wrote to Dr Jeff Severinghaus about some contradictory information on their website which was fixed up to remove the contradiction, but unfortunately I feel in the wrong direction.

So we have the interesting situation that I as a so-called “warmist” am in agreement with Roy Spencer , who’s supposed to be a sceptic, but many who I would describe as a rabid deniers are more in agreement with what at least some mainstream scientists are arguing.

Dr Spencer being right on this point doesn’t, on the face of it, actually help the sceptics cause. However,it must be worth getting everything right to minimise the uncertainties involved with climate models. It would be an interesting test of these models to see what would happen to the lapse rate if they removed all the GH gases from them.

tempterrain,
I don’t usually touch this topic but I think some pointers would help.

The Talkshop has many posts and comment threads dealing one way or another with lapse rate. This thread is not a good one if you want some general clarity. (>1,000 posts on this site)

By lapse rate you mean what exactly? Of course there is a lapse rate, it’s the shape where the arguments start.

A good minder is look at the temperature vs. altitude plots of Venus, Earth and Jupiter, probes have visited two of those, we live on the other. All three have a similar profile, with troposphere in which is a linear vs. altitude characteristic. Venus has an essentially pure CO2 atmosphere and Jupiter devoid of CO2. (plots are on the Talkshop)https://tallbloke.files.wordpress.com/2011/12/venus-1-small.png?w=500&h=377
(you will want to independently check, I did the plots)

What you will find difficult is discovering a real example of a pure radiative profile lapse rate, or even close to that.

Be an idea to go look at radiosonde data. You will also find temperature inversions within the troposphere, lots of interesting stuff and reasons, not all understood.

The Talkshop has “endless” discussions about the part played by gravity, gas physics etc., I think most of these would confuse you. (sure as hell confuse me from time to time)

If you are brave and are prepared to dig for yourself, getting a feel for the Hurt exponent etc. is a good move. A subject not covered on the Talkshop yet. In essence most natural processes are not Gaussian random which means the variability is larger than “normal” stats suggest, particularly tomorrow will not be the opposite of today but there are “periods of” wet, hot, dry, cold, wind etc.
A lot not known yet things fit, such as the maximum entropy idea, scaling and so on.
Start digging point, can find hundreds of serious links and papers,http://itia.ntua.gr/en/docinfo/537/

I’m not a trained climate scientist, although my background is in Physics. Its more a question of deciding who to believe.

Roy Spencer is one of the more sensible of the climate sceptics and his explanation of the GH effect lines up with my understanding. So, at the moment, I’m tending to believe he’s probably right.

I’m less clear on why he believes the feedbacks of clouds are likely to be negative, meaning that climate sensistivity to CO2 is going to be lower than others might expect. I hope he’s right – but I guess we’ll have to see about that.